2024年度セミナー Seminars in 2024
今年度後期は木曜日午後２時半から生産技術研究所（柏キャンパス）研究実験棟Ⅰの３階大会議室または小会議室で行います。 このセミナーの他にも、毎週月曜日午後１時から本郷キャンパス理学部１号館206号室で統計力学セミナーにも参加しています。
The second half of this school year, we do regular seminars from 2:30pm, every Thursday at the large conference room or the small conference roon on the third floor of Research and Testing Complex I, Institute of Industrial Science (Building 30 of this map). We also attend the seminar series Statistical Physics seminar series from 1:00pm every Monday at Room 206, Science Bldg.in the Hongo campus.
| 日程 Date |
時間 Time |
講演者 Speaker |
演題・Abstract Title and Abstract |
| 4月24日(水) Wed, April 24 |
10:30 |
Tomio Petrosky さん（テキサス大） Dr. Tomio Petrosky (U. Texas at Austin) |
Quantitative analysis of the spectral gap of Liouville operator at resonance singularities of a non-integrable system with few degrees of freedom in terms of the effective Liouvillian Abstract |
| 4月24日(水) Wed, April 24 |
15:00 |
中井雄介さん（京大基研） Yusuke Nakai (YITP) |
Topological enhancement of non-normality in non-Hermitian skin effects Abstract |
| 5月8日(水) Wed, May 8 |
10:30 |
Donghoon Kim さん（理研 / RIKEN) | Thermal and Spatial Entanglement of Exotic Quantum Impurity Systems Abstract |
| 5月15日(水) Wed, May 15 |
10:30 |
金子隆威さん（上智大） Dr. Ryui Kaneko (Sophia U.) |
Quantum search in a hypercube lattice model Abstract |
| 5月22日(水) Wed, May 22 |
10:30 |
小林海翔さん（東大） Kaito Kobayashi (U. Tokyo) |
Quantum reservoir probing: an inverse paradigm of reservoir computing for exploring quantum many-body physics Abstract |
| 5月29日(水) Wed, May 29 |
10:30 |
白石航暉さん（東大） Koki Shiraishi (U. Tokyo) |
Quantum master equation for many-body systems: Derivation based on the Lieb-Robinson bound Abstract |
| 6月5日(水) Wed, June 5 |
10:30 |
Dr. Eva-Maria Graefe (Imperial College London) | Chaos in quantum systems with non-Hermitian and PT-symmetric Hamiltonians Abstract |
| 6月12日(水) Wed, June 12 |
10:30 |
渡邉光さん（東大先端研） Dr. Hikaru Watanabe (RCAST, U. Tokyo) |
Pitaevskii relation connecting linear and rectification responses Abstract |
| 6月19日(水) Wed, June 19 |
10:30 |
Zhenyu Xiao（Beijing U.) | Spin Space Groups: Full Classification and Applications Abstract |
| 6月26日(水) Wed, June 26 |
10:30 |
瀬川悦生さん（横国大） Dr. Etsuo Segawa (Yokohama Natl. U.) |
T.B.A. Abstract |
| 7月10日(水) Wed, July 10 |
10:30 |
宮下精二さん（東大・日本物理学会） Dr. Seiji Miyashita (U. Tokyo, PSJ) |
Quantum manipulation to cross an energy barrier without tunneling effect Abstract |
| 7月17日(水) Wed, July 17 |
10:30 |
奥川亮さん（東京理科大） Dr. Ryo Okugawa (Tokyo U. Science) |
Dynamical quantum phase transitions in topological crystalline insulators Abstract |
| 7月24日(水) Wed, July 24 |
10:30 |
Dr. Avadh Saxena (Los Alamos Natl. Lab.) | Hopfions in Condensed Matter: Anisotropic Heisenberg Magnets Abstract Room different from the usual |
| 7月24日(水) Wed, July 24 |
14:00 Afternoon of the same day |
Archak Purkayastha (Ind. Inst. Tech.) | Quantum transport and exceptional points of transfer matrix Abstract Room different from the usual |
| 10月23日(水) Wed, October 23 |
10:30 |
高橋惇さん（東大物性研） Dr. Takahashi Jun (ISSP, U. Tokyo） |
NP-hardness of Curing the Negative-Sign Problem with Clifford Circuits Abstract |
| 11月21日(木) Thu, November 21 |
14:30 |
Dr. Guancong Ma (Hong Kong Baptist University) | Non-Hermitian Physics with Acoustic and Mechanical Waves Abstract |
| 11月28日(木) Thu, November 28 |
14:30 |
井村健一郎さん（東大生研） Dr. Ken-Ichiro Imura (IIS, U. Tokyo) |
Wave-packet and entanglement dynamics in a non-Hermitian system Abstract |
| 12月04日(水) Wed, December 04 |
14:30 |
小川直哉さん（前・名大） Mr. Naoya Ogawa (Nagoya U.) |
Position-Momentum Uncertainty Relation for Errors with Gaussian Wave-packet Basis Abstract |
| 12月12日(木) Thu, December 12 |
14:30 |
沼澤宙朗さん（東大） Dr. Tokiro Numasawa (U.Tokyo) |
The SYK model with dissipation Abstract |
| 1月30日(木) Thu, January 30 |
14:30 |
Prof. Igor Herbut（Simon Fraser U., Canada） | SO(8) unified theory of two-dimensional interacting Dirac fermions Abstract |
| 2月13日(木) Thu, January 30 |
14:30 |
Prof. Fabio Bagarello (U. Palermo, Italy） | A brief introduction to non Hermitian Hamiltonians and on their dynamics: the role of ladder operators Abstract |
第０１回 No. 01
講師 Lecturer：Tomio Petrosky さん（テキサス大）Dr. Tomio Petrosky (U. Texas at Austin)日時 Date：２０２４年０４月２４日（水）１０時３０分〜 Wednesday, 24th April 2024, 10:30 JST ~
場所 Place：東京大学生産技術研究所 研究実験棟Ｉn301号室 n301, Research and Testing Complex I, IIS, the University of Tokyo
演題 Title：Quantitative analysis of the spectral gap of Liouville operator at resonance singularities of a non-integrable system with few degrees of freedom in terms of the effective Liouvillian
要旨 Abstract：
We analyze the motion of a nonlinear, nonintegrable classical Hamiltonian system with few degrees of freedom with a resonance singularity. Poincaré showed that in such systems there are not enough number of independent invariants of motion required to integrate the equation of motion. This is the so-called Poincaré's non-integrable theorem.
In this lecture, we will analyze such systems from a new viewpoint, that is the eigenvalue problem of the Liouville operator in the Liouville equation to analyze the behavior of the state functions, rather than following the trajectory. This shows that it is possible to perform analytical and quantitative analysis of the non-integrable systems with the resonance singularities. In that case, we will show that non-linear eigenvalue problem of the collision operator which plays a central role in the analysis of nonequilibrium statistical mechanics (which is also called the effective Liouvillian) to analyze the original linier eigenvalue problem of the Liouvillian.
As an example, we will analyze a system in which a nonlinear pendulum is coupled to a harmonic oscillator and find that the spectrum of the Liouvillian causes level repulsion at the resonant point, creating a gap in the spectrum.
第０２回 No. 02
講師 Lecturer：中井雄介さん（京大基研）Yusuke Nakai (YITP)日時 Date：２０２４年０４月２４日（水）１５時００分〜 Wednesday, 24th April 2024, 15:00 JST ~
場所 Place：東京大学生産技術研究所 研究実験棟Ｉ大会議室 The large conference room, Research and Testing Complex I, IIS, the University of Tokyo
演題 Title：Topological enhancement of non-normality in non-Hermitian skin effects
要旨 Abstract：
The non-Hermitian skin effects are representative phenomena intrinsic to non-Hermitian systems: the energy spectra and eigenstates under the open boundary condition (OBC) drastically differ from those under the periodic boundary condition (PBC). Whereas a non-trivial topology under the PBC characterizes the non-Hermitian skin effects, their proper measure under the OBC has not been clarified yet. In this talk, we reveal that topological enhancement of non-normality under the OBC accurately quantifies the non-Hermitian skin effects. Correspondingly to spectrum and state changes of the skin effects, we introduce two scalar measures of non-normality and argue that the non-Hermitian skin effects enhance both macroscopically under the OBC. We also show that the enhanced non-normality correctly describes phase transitions causing the non-Hermitian skin effects. The topological enhancement of non-normality governs the perturbation sensitivity of the OBC spectra and the anomalous time-evolution dynamics through the Bauer-Fike theorem. This talk is based on Ref. [1].
第０３回 No. 03
講師 Lecturer：Donghoon Kim さん（理研 / RIKEN)日時 Date：２０２４年０５月０８日（水）１０時３０分〜 / Wednesday, 08th May 2024, 10:30 JST ~
場所 Place：東京大学生産技術研究所 研究実験棟Ｉ大会議室 The large conference room, Research and Testing Complex I, IIS, the University of Tokyo
演題 Title：Thermal and Spatial Entanglement of Exotic Quantum Impurity Systems
要旨 Abstract：
The quantum impurity system is a strongly correlated system that exhibits various non-Fermi liquid phases and has become experimentally engineerable due to advances in nanotechnology. A primary characteristic of this system originates from the quantum coherent screening of the impurity spin by surrounding electrons.
In this work, we theoretically analyze this quantum coherent screening by using quantum entanglement, and suggest how to observe it in experiments. We develop a method to compute the entanglement negativity between the impurity and electrons in spin-1/2 impurity problems, based on the boundary conformal field theory and numerical renormalization group [1]. We examine the thermal entanglement and its spatial distribution, referred to as the screening cloud, in various exotic quantum impurity systems [1,2]. Our findings at low temperatures reveal a universal behavior in the entanglement, characterized by a power-law thermal decay with a fractional exponent. The value of this exponent is intricately linked to the scaling dimension of the boundary operator that represents the impurity spin. Moreover, we observe that the spatial distribution of entanglement follows a universal power-law structure, mirroring the exponent identified in the thermal decay. Our analysis identifies the coexistence of distinct (non-)Fermi liquids within the distribution, which are organized into concentric shells centered around the impurity. As the temperature rises, these outer shells are sequentially diminished, with the outermost shell at any given temperature dictating the system's overall phase.
参考文献 References
[1] D. Kim, J. Shim, and H.-S. Sim, Phys. Rev. Lett. 127, 226801 (2021)
[2] J. Shim, D. Kim, and H.-S. Sim, Nat. Commun. 14, 3521 (2023)
第０４回 No. 04
講師 Speaker:金子隆威さん（上智大）Dr. Ryui Kaneko (Sophia U.)日時 Date: ２０２４年５月１５日（水）１０時３０分〜 / Wednesday, 15th May 2024, 10:30 JST ~
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus) Large Conference Room
演題 Title: Quantum search in a hypercube lattice model
要旨 Abstract: Quantum lattice models can be used to analyze many physical systems, such as semiconductor quantum wires, carbon nanotubes or topological insulators. Here we consider a tight-binding model of a hypercubic lattice in n dimensions, which correspond to the space of n-qubit words. The quantum propagation of a single particle in this lattice can be related to the search of an n-qubit word. We show that the time it takes to find an n-qubit word using quantum propagation is proportional to √(2^n ), whereas a classical search would take a time proportional to 2^n. We discuss an implementation this model in an IBM quantum computer and compare results with Grover’s quantum search algorithm, which is one of the best-known quantum search algorithms.
第０５回 No. 05
講師 Speaker:小林海翔さん（東大） Kaito Kobayashi (U. Tokyo)日時 Date：２０２４年０５月２２日（水）１０時３０分〜 / Wednesday, 22nd May 2024, 10:30 JST ~
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus) Large Conference Room
演題 Title: Quantum reservoir probing: an inverse paradigm of reservoir computing for exploring quantum many-body physics
要旨 Abstract:
Artificial neural networks have established themselves as a cornerstone of the modern information-centric society. However, their training incurs significant computational overhead. A recent paradigm shift involves the physical realization of these networks, where a physical system embodies a neural network with fixed weights, eliminating the need for optimization. Physical reservoir computing [1] exemplifies this approach. Here, input data are nonlinearly transformed by nonlinear phenomena in a system referred to as a “physical reservoir”. The computational efficacy is deeply connected to the unique properties of the physical reservoir, motivating exploration of diverse platforms like magnetic [2] and quantum systems [3].
Interestingly, the diverse computational performance exhibited by various types of physical reservoirs suggests an alternative research direction; namely, examining the physical system itself through computational efficiency when employed as a physical reservoir. In this talk, we formalize this novel approach to investigating quantum systems as quantum reservoir probing (QRP) [4,5]. Here, random information is locally introduced into the quantum system, and we then attempt to deduce this input from the expectation value of a local operator through a linear transformation. The accuracy of this estimation serves as a measure of information propagation. We demonstrate that the QRP can effectively capture how information is distributed across various degrees of freedom at individual points in time. Furthermore, we observe that the dynamics of information propagation exhibit different characteristics in distinct quantum phases, serving as a marker of quantum phase transitions. The QRP framework holds promise for unveiling novel insights into a broad spectrum of exotic quantum many-body phenomena.
参考文献 References
[1] H. Jaeger and H. Haas, Science 304, 78-80 (2004).
[2] K. Kobayashi and Y. Motome, Sci. Rep. 13, 15123 (2023).
[3] K. Fujii and K. Nakajima, Phys. Rev. Applied 8, 024030 (2017).
[4] K. Kobayashi and Y. Motome, arXiv:2308.00898 (2023).
[5] K. Kobayashi and Y. Motome, arXiv:2402.07097 (2024).
第０６回 No. 06
講師 Speaker:白石航暉さん（東大） Koki Shiraishi (U. Tokyo)日時 Date：２０２４年０５月２９日（水）１０時３０分〜 / Wednesday, 29th May 2024, 10:30 JST ~
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus) Large Conference Room
演題 Title: Quantum master equation for many-body systems: Derivation based on the Lieb-Robinson bound
要旨 Abstract:
The theory of open quantum systems is now applied to the analysis of various transport phenomena. Such interesting phenomena mostly occur in many-body systems. However, there are fundamental problems, such as the violation of the rotating-wave approximation, and technical problems, such as computational complexity, in applying methods of open quantum systems to many-body systems.
The local Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) quantum master equation is a powerful tool for the study of open quantum many-body systems. However, its microscopic derivation applicable to many-body systems is available only in limited cases of weak internal couplings, and it has yet to be fully understood under what microscopic conditions the local GKSL equation is valid.
In this seminar, we introduce a microscopic derivation of the local GKSL equation based on the Lieb-Robinson bound. Then, we present our numerical results to illustrate that the validity of the local GKSL equation depends on the relaxation time of the environment, the time scale of the interaction between the environment and the system, and the time scale of the propagation of the influence of the environment in the system. Finally, we will also give a quick introduction to related results in preparation, including an example where the rotating-wave approximation is justifiable even for many-body systems.
参考文献 References
K. Shiraishi, M. Nakagawa, T. Mori, and M. Ueda. arXiv:2404.14067
第０７回 No. 07
講師 Speaker: Dr. Eva-Maria Graefe (Imperial College London)日時 Date：２０２４年０６月５日（水）１０時３０分〜 / Wednesday, 5th June 2024, 10:30 JST ~
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus) Large Conference Room
演題 Title: Chaos in quantum systems with non-Hermitian and PT-symmetric Hamiltonians
要旨 Abstract:
In recent years there has been ever growing interest in the use of non-Hermitian Hamiltonians as effective models for quantum systems with loss and gain. In particular, PT-symmetric systems, characterised by a certain balance of loss and gain, have attracted considerable attention. It is an interesting and mostly open question how non-Hermiticity and PT-symmetry interact with chaos. In this talk I will discuss various aspects of this question for example systems.
第０８回 No. 08
講師 Speaker: 渡邉光さん（東大先端研）Dr. Hikaru Watanabe (RCAST, U. Tokyo)日時 Date：２０２４年０６月１２日（水）１０時３０分〜 / Wednesday, 12th June 2024, 10:30 JST ~
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus) Large Conference Room
演題 Title: Pitaevskii relation connecting linear and rectification responses
要旨 Abstract:
Recent advancements in light technology have broadened the scope of correlation between magnetism and light. A prime example is the control of magnetization using ultrashort pulse light [1]. By tuning the frequency of light, this magnetization control can be achieved with minimal thermal losses by using the inverse Faraday effect, where effective magnetic fields are induced by light. The effect, rectification response (a nonlinear response) triggered by optical fields, is intimately linked with the linear response coefficient known as the optical Hall conductivity [2]. This presentation zeroes in on the Pitaevskii relation, which bridges these nonlinear and linear responses. While past studies frequently relied on empirically derived effective non-equilibrium free energy, this research microscopically establishes the Pitaevskii relation from the response theory. As an illustrative application, we delve into several uncovered Pitaevskii relations [3].
References
[1] A. Kirilyuk, A. V. Kimel, and T. Rasing, Ultrafast Optical Manipulation of Magnetic Order, Rev. Mod. Phys. 82, 2731 (2010).
[2] L. P. Pitaevskii, Sov. Phys. JETP 12, 1008 (1961);J. P. van der Ziel et al., Optically-Induced Magnetization Resulting from the Inverse Faraday Effect, Phys. Rev. Lett. 15, 190 (1965).
[3] H. Watanabe and A. Daido, Generalized Pitaevskii relation between rectifying and linear responses: its application to reciprocal magnetization induction, arXiv:2404.07489.
第０９回 No. 09
講師 Speaker: Zhenyu Xiaoさん（北京大学・Beijing U.)日時 Date：２０２４年０６月１９日（水）１０時３０分〜 / Wednesday, 19th June 2024, 10:30 JST ~
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus) Large Conference Room
演題 Title: Spin Space Groups: Full Classification and Applications
要旨 Abstract:
We exhaust all the spin-space symmetries, which fully characterize collinear, non-collinear, commensurate, and incommensurate spiral magnetism, and investigate enriched features of electronic bands that respect these symmetries. We achieve this by systematically classifying the so-called spin space groups (SSGs) - joint symmetry groups of spatial and spin operations that leave the magnetic structure unchanged. Generally speaking, they are accurate (approximate) symmetries in systems where spin-orbit coupling (SOC) is negligible (finite but weaker than the interested energy scale); but we also show that specific SSGs could remain valid even in the presence of a strong SOC. By representing the SSGs as O(N) representations, we - for the first time - obtain the complete classifications of 1421, 9542, and 56 512 distinct SSGs for collinear (N=1), coplanar (N=2), and non-coplanar (N=3) magnetism, respectively. SSG not only fully characterizes the symmetry of spin d.o.f., but also gives rise to exotic electronic states, which, in general, form projective representations of magnetic space groups (MSGs). Surprisingly, electronic bands in SSGs exhibit features never seen in MSGs, such as nonsymmorphic SSG Brillouin zone (BZ), where SSG operations behave as glide or screw when act on momentum and unconventional spin-momentum locking, which is completely determined by SSG, independent of Hamiltonian details. To apply our theory, we identify the SSG for each of the 1595 published magnetic structures in the MAGNDATA database on the Bilbao Crystallographic Server. Material examples exhibiting aforementioned novel features are discussed with emphasis. We also investigate new types of SSG-protected topological electronic states that are unprecedented in MSGs.
Reference: https://arxiv.org/abs/2307.10364
第１０回 No. 10
講師 Speaker: 瀬川悦生さん（横国大）Dr. Etsuo Segawa (Yokohama Natl. U.)日時 Date：２０２４年０６月２６日（水）１０時３０分〜 / Wednesday, 26th June 2024, 10:30 JST ~
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus) Large Conference Room
演題 Title: T.B.A
要旨 Abstract:
T.B.A.
第１１回 No. 11
講師 Speaker: 宮下精二さん（東大・日本物理学会）Dr. Seiji Miyashita (U. Tokyo, PSJ)日時 Date：２０２４年０７月１０日（水）１０時３０分〜 / Wednesday, 10th July 2024, 10:30 JST ~
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus) Large Conference Room
演題 Title: Quantum manipulation to cross an energy barrier without tunneling effect
要旨 Abstract:
Real-time quantum dynamics is one of the most important subjects for manipulations of quantum states, and it has been studied in various topics [1]. For example, the mechanism of Landau-Zener mechanism with ac-field [2] and also under a sweeping field were studied [3]. Conveyance of quantum particles in real time has been important topics [4]. Real time dynamics plays important roles also in the quantum annealing process [4]. Non-hermitian properties in infinite systems is also important topics [5]. Passing through an energy barrier is one of the most remarkable topics of physics. Recently, a new protocol to overcome an energy barrier with a shaped pulse has been found [6]. Here, we discuss the last topic studying a magnetic system of spin S with an energy barrier, such as rare-earth elements and their compounds, single molecule magnets with uniaxial anisotropy, and more generally any other anisotropic quantum system made of single or multiple objects with discrete energy levels. Till now, the reversal of the magnetization of such systems required a very strong field to diminish the barrier (Stoner-Wohlfarth mechanism) or the quantum tunneling by a significant transverse field at resonance. Here, we show that another very simple method exists. It consists in the application of a particular sequence of electromagnetic radiations (shaped field). This produces oscillations of the Rabi type and pass above the barrier is realized "giant quantum oscillations above the barrier (GQOAB)". We also study an alternate protocol and discuss a classical limit of the protocol showing that "giant classical oscillations above the barrier (GCOAB)" can also be designed. This approach would open up new directions of research in quantum information protocols.
[1] S. Miyashita, J. Computational and Theoretical Nanoscience 8, 919 (2011).
S. Miyashita, Collapse of Metastability, Springer-Nature (2022).
[1] S. Miyashita, J. Phys. Soc. Jpn. 76, 104003 (2007). S. Miyashita, K. Saito and H. De Raedt, Phys. Rev. Lett. 80, 1525-1528 Feb. (1998).
[2}T. Hatomura, B. Barbara and S. Miyashita, Phys. Rev. Lett. 116, (2016) 037203, and Phys. Rev. B 96,134309 (2017).
[3] S. Miyashita, J. Phys. Soc. Jpn. 76, 104003 (2007). S. Morita, Y. Teranishi and S. Miyashita, in preparation.
[4] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998). S. Morita, J. Phys. Soc. Jpn. 76, 104001 (2007).
[5] N. Hatano, K. Sasada, H. Nakamura, and T. Petrosky, Prog. Theor. Phys. 119, 187 (2008).
[6] S. Miyashita and B. Barbara, Phys. Rev. Lett. 131, 066701 (2023), and Phys. Rev. B 109, 104301 (2024). Rachel Berkowitz, Physics 16 s118 (2023).
第１２回 No. 12
講師 Speaker: 奥川亮さん（東京理科大）Dr. Ryo Okugawa (Tokyo U. Science)日時 Date：２０２４年０７月１７日（水）１０時３０分〜 / Wednesday, 17th July 2024, 10:30 JST ~
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus) Large Conference Room
演題 Title: Dynamical quantum phase transitions in topological crystalline insulators
要旨 Abstract:
A dynamical quantum phase transition (DQPT) is a nonequilibrium counterpart of equilibrium phase transitions in quantum dynamics. In quenched systems, DQPTs emerge through zeros of the Loschmidt amplitude, which are analogous to the Fisher zeros of canonical partition functions. While it is difficult to clarify the conditions under which DQPTs necessarily occur, DQPTs that can be predicted from band topology have been elucidated in topological systems. We show that such DQPTs can occur in topological crystalline insulators protected by mirror symmetry. Additionally, we present topological invariants that characterize the DQPTs. Furthermore, we reveal the behavior of topologically characterized DQPTs by using lattice models for two-dimensional topological crystalline insulators.
Reference
R. Okugawa, H. Oshiyama, and M. Ohzeki, Phys. Rev. Research 3, 043064 (2021).
第１３回 No. 13
講師 Speaker: Dr. Avadh Saxena (Los Alamos Natl. Lab.)日時 Date：２０２４年０７月２４日（水）１０時３０分〜 / Wednesday, 24th July 2024, 10:30 JST ~
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）小会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus) Small Conference Room
演題 Title: Hopfions in Condensed Matter: Anisotropic Heisenberg Magnets
要旨 Abstract:
Nontrivial topological defects such as knotted solitons called hopfions have been observed in a variety of materials including chiral magnets, nematic liquid crystals and even in ferroelectrics as well as studied in other physical contexts such as Bose-Einstein condensates. These topological entities can be modeled using the relevant physical variable, e.g., magnetization, polarization or the director field. Specifically, we find exact static soliton solutions for the unit spin vector field of an inhomogeneous, anisotropic three-dimensional (3D) Heisenberg ferromagnet and calculate the corresponding Hopf invariant H analytically and obtain an integer, demonstrating that these solitons are indeed hopfions [1]. H is a product of two integers, the first being the usual winding number of a skyrmion in two dimensions, while the second encodes the periodicity in the third dimension. We also study the underlying geometry of H, by mapping the 3D unit vector field to tangent vectors of three appropriately defined space curves. Our analysis shows that a certain intrinsic twist is necessary to yield a nontrivial topological invariant: linking number [2]. Finally, we focus on the formation energy of hopfions to study their properties for potential applications.
Reference:
[1] R. Balakrishnan, R. Dandoloff, and A. Saxena, Phys. Lett. A 480 128975 (2023).
[2] R. Balakrishnan, R. Dandoloff and A. Saxena, Phys. Lett. A 493, 129261 (2024).
第１４回 No. 14
講師 Speaker: Dr. Archak Purkayastha (Ind. Inst. Tech.)日時 Date：２０２４年０７月２４日（水）１４時００分〜 / Wednesday, 24th July 2024, 14:00 JST ~
Note that this takes place in the afternoon of the same day of the No. 13 seminar.
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）小会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus) Small Conference Room
演題 Title: Quantum transport and exceptional points of transfer matrix
要旨 Abstract:
We consider fermionic chains with finite-range hopping. The energy dispersion of such Hermitian Hamiltonian can be obtained from the transfer matrix of the system, which is non-Hermitian by construction. Transport through such chains can be classified in terms of how the conductance scales with the chain length, when a small chemical potential bias is applied via coupling to two baths at two ends. We discuss how the conductance scaling with system length is governed by spectral properties of the transfer matrix. This reveals counterintuitive universal transport properties near band edges of the system, stemming from exceptional points of the transfer matrix that occur at every band edge.
第１５回 No. 15
講師 Speaker：高橋惇（Takahashi Jun）さん（東大物性研 / ISSP, U. Tokyo）日時 Date：２０２４年１０月２３日（水）１０時３０分〜 / Wednesday, 23rd October 2024, 10:30 JST -
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus)Large Conference Room
演題 Title：NP-hardness of Curing the Negative-Sign Problem with Clifford Circuits
要旨 Abstract：
The negative-sign problem is the difficulty one faces when trying to use Monte Carlo sampling to study thermal states of quantum systems. It not only is a practical obstacle for studying quantum systems classically but also provides a theoretical framework for considering an interesting middle ground of "stoquastic" systems [1] where a quantum Hamiltonian is not entirely classical but nevertheless admits Monte Carlo sampling without a sign problem. Since the Monte Carlo sign problem is a basis dependent property, it has remained rather mysterious when a quantum system can and cannot be made sign-problem free i.e. stoquastic with some efficiently computable basis rotation [2]. In this talk, I will consider curing the sign problem by using Clifford circuits, which is a framework that is *barely* classically simulable. To be more precise, while any Clifford circuit basis rotation can be computed classically in polynomial time, if we add just one other type of gate (T-gates) such computation will become equivalent to universal quantum computation. We show that this class can cure the sign problems of many interesting classes including the J1-J2 chain [3] which is traditionally considered to be frustrated. We prove the computational complexity of finding such sign-curing Clifford circuits is NP-hard, which is the first result for a global unitary transformation family [4], as well as optimality results of the previously discovered sign-curing for the J1-J2 chain [3].
Reference:
[1] T. Cubitt and A. Montanaro, SIAM J. Comput. 45, 268 (2016).
[2] M. Marvian, D. Lidar, and I. Hen, Nat. Commun. 10, 1571 (2019).
[3] T. Nakamura, Phys. Rev. B 57, R3197 (1998).
[4] J. Takahashi and M. Marvian, in prep.
第１６回 No. 16
講師 Speaker：馬冠聰（Guancong Ma） さん（Hong Kong Baptist University）日時 Date：２０２４年１１月２１日（木）１４時３０分〜 / Thursday, 21st November 2024, 14:30 JST -
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus)Large Conference Room
演題 Title：Non-Hermitian Physics with Acoustic and Mechanical Waves
要旨 Abstract：
Non-Hermitian physics has recently captivated much attention of physicists and engineers across many realms. The realization of non-Hermitian phenomena demands precise control over the energy exchange between the system and external environments, which remain challenging in many areas. In this talk, I will show how to realize Hermitian and non-Hermitian tight-binding models using acoustic and mechanical wave systems. Topics to be discussed include exceptional points and their topological characterizations [1–3], non-Hermitian skin effects [4,5], and non-Hermitian delocalization [6,7].
Reference:
[1] W. Tang, X. Jiang, K. Ding, Y.-X. Xiao, Z.-Q. Zhang, C. T. Chan, and G. Ma, Exceptional nexus with a hybrid topological invariant, Science 370, 1077 (2020).
[2] W. Tang, K. Ding, and G. Ma, Experimental realization of non-Abelian permutations in a three-state non-Hermitian system, Natl. Sci. Rev. 9, nwac010 (2022).
[3] W. Tang, K. Ding, and G. Ma, Realization and topological properties of third-order exceptional lines embedded in exceptional surfaces, Nat. Commun. 14, 6660 (2023).
[4] X. Wang, W. Wang, and G. Ma, Extended topological mode in a one-dimensional non-Hermitian acoustic crystal, AAPPS Bull. 33, 23 (2023).
[5] W. Wang, M. Hu, X. Wang, G. Ma, and K. Ding, Experimental Realization of Geometry-Dependent Skin Effect in a Reciprocal Two-Dimensional Lattice, Phys. Rev. Lett. 131, 207201 (2023).
[6] W. Wang, X. Wang, and G. Ma, Non-Hermitian morphing of topological modes, Nature 608, 50 (2022).
[7] W. Wang, X. Wang, and G. Ma, Extended State in a Localized Continuum, Phys. Rev. Lett. 129, 264301 (2022).
第１７回 No. 17
講師 Speaker：井村健一郎さん（東大生研）Dr. Ken-Ichiro Imura（Institute of Industrial Sciente, U. Tokyo）日時 Date：２０２４年１１月２８日（木）１４時３０分〜 / Thursday, 28th November 2024, 14:30 JST -
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus)Large Conference Room
演題 Title：Wave-packet and entanglement dynamics in a non-Hermitian system
要旨 Abstract：
n this talk I will discuss the wave-packet and entanglement dynamics in the non-Hermitian Hatano-Nelson model [1]; one-dimensional model with asymmetric hopping. If this asymmetry is not too weak, the wave-packet dynamics in this system becomes effectively unidirectional and spreading of the wave packet is much suppressed compared with the Hermitian case.
In Hermitian quantum system, interference of the complex valued wave function makes the dynamics of wave packet very different from that of classical (gaussian) diffusion. Here, in the non-Hermitian case the spreading of the wave packet on top of its unidirectional motion becomes pseudo classical (gaussian) [2].
In the entanglement dynamics, collapse of the superposition due to a finite imaginary part in the eigenenergy leads to a non-monotonic evolution [3].
Reference:
[1] N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996). https://doi.org/10.1103/PhysRevLett.77.570
[2] T. Orito and K.-I. Imura, Phys. Rev. B 105, 024303 (2022). https://doi.org/10.1103/PhysRevB.105.024303
[3] T. Orito and K.-I. Imura, Phys. Rev. B 108, 214308 (2023). https://doi.org/10.1103/PhysRevB.108.214308
第１８回 No. 18
講師 Speaker：小川直哉さん（前・名大）Mr. Naoya Ogawa（Nagoya U.）日時 Date：２０２４年１２月４日（水）１４時３０分〜 / Wednesday, 4th December 2024, 14:30 JST -
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus)Large Conference Room
演題 Title：Position-Momentum Uncertainty Relation for Errors with Gaussian Wave-packet Basis
要旨 Abstract：
The Lee-Tsutsui (LT) formalism, a contemporary formulation of uncertainty relations in quantum mechanics, has been recently proposed by Lee and Tsutsui. The LT formalism is universal in the sense that it is claimed to encompass various types of the conventional uncertainty relations, including the Kennard-Robertson, Arthurs-Kelly-Goodman, Ozawa, and Watanabe-Sagawa-Ueda inequalities. The LT formalism introduces two types of the errors and inequalities, the Lee-Tsutsui (LT) [1,2] and Lee [3] types. The errors in the LT formalism involve only pre- and post-measurement quantities ensuring their clear operational interpretations. However, the abstract nature of the LT formalism poses challenges in providing concrete examples of its practical applications.
Also, Gaussian wave-packet basis (GWB) [4,5] is a basis composed of the states that have the definite width both for position and momentum and is indeed a basis. GWB can serve as an effective tool for performing joint measurement of position and momentum, and it provides a Positive-Operator-Valued-Measure (POVM) measurement.
In our work [6], we apply the LT formalism to GWB by considering the joint measurement of position and momentum given by a GWB on a state represented by another GWB, and calculating the corresponding LT and Lee inequalities. Our result shows that while the LT inequality yields a trivial lower bound, the Lee inequality provides a nontrivial lower bound that is consistent with the conventional Heisenberg's uncertainty principle and is always saturated.
Reference:
[1] J. Lee and I. Tsutsui, A universal formulation of uncertainty relation for errors, Phys. Lett. A 526, 129962 (2024). https://doi.org/10.1016/j.physleta.2024.129962
[2] J. Lee and I. Tsutsui, Uncertainty Relation for Errors Focusing on General POVM Measurements with an Example of Two-State Quantum Systems, Entropy 2020, 22, 1222 (2020). https://doi.org/10.3390/e22111222
[3] J. Lee, A Universal Formulation of Uncertainty Relation for Errors under Local Representability, arXiv:2203.08197 [quant-ph] (2022). https://doi.org/10.48550/arXiv.2203.08197
[4] R. J. Glauber, The quantum theory of optical coherence, Phys. Rev. 130, 2529 (1963). https://doi.org/10.1103/PhysRev.130.2529
[5] K.-y. Oda and J. Wada, A complete set of Lorentz-invariant wave packets and modified uncertainty relation, Eur. Phys. J. C 81, 751 (2021). https://doi.org/10.1140/epjc/s10052-021-09482-1
[6] K.-y. Oda and N. Ogawa, Gaussian Formalism: Concrete Realization of Joint Measurement for Heisenberg's Uncertainty Relation for Errors, arXiv:2403.19440 [hep-ph] (2024). https://doi.org/10.48550/arXiv.2403.19440
第１９回 No. 19
講師 Speaker：沼澤宙朗さん（東大・物性研）Dr. Tokiro Numasawa (ISSP, U.Tokyo)日時Date：２０２４年１２月１２日（木）１４時３０分〜 / Thursday, 12th December 2024, 14:30 JST -
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus)Large Conference Room
演題Title：The SYK model with dissipation
要旨Abstract：
We study the Lindbladian dynamics of the Sachdev-Ye-Kitaev (SYK) model, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. In the limit of large N, where N is the number of Majorana fermion operators, the SYK Lindbladians are analytically tractable, and we obtain their stationary Green's functions, from which we can read off the decay rate. For finite N, we also study the distribution of the eigenvalues of the SYK Lindbladians. Then, we consider the time evolution of the dissipative form factor, which quantifies the average overlap between the initial and time-evolved density matrices as an open quantum generalization of the Loschmidt echo. We find that the dissipative form factor exhibits dynamical quantum phase transitions. We analytically demonstrate a discontinuous dynamical phase transition in the limit of a large number of fermion flavors, which is formally akin to the thermal phase transition in the two-coupled SYK model between the black-hole and wormhole phases. Furthermore, we numerically show that signatures of the dynamical quantum phase transitions remain to appear even in the finite number of fermion flavors. Finally, we show the symmetry classification of the SYK Lindbladians. If time allows, I will comment on possible connections to de Sitter wormholes. This talk is based on the papers arxiv:2112.13489, arXiv:2210.04093 and arXiv:2212.00605.
第２０回 No. 20
講師 Speaker：Prof. Igor Herbut (Simon Fraser U., Canada)日時Date：２０２５年１月３０日（木）１４時３０分〜 / Thursday, 30th January 2025, 14:30 JST -
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus)Large Conference Room
演題Title：SO(8) unified theory of two-dimensional interacting Dirac fermions
要旨Abstract：
Dirac fermions appear as low-energy quasiparticle excitations in many condensed matter systems of current interest. They are often weakly interacting, as in graphene for example, but at strong interactions they can also exhibit many ordered ground states by going through phase transitions at which gapless Dirac fermions play a crucial role. A prime example of such a transition occurs in the standard Hubbard model on honeycomb lattice at half filling, which has a semimetal - Mott insulator transition in the so-called Heisenberg-Gross-Neveu universality class. (1) I will discuss a unifying theory of all leading order parameters for Dirac systems in two-dimensions, based on the hidden SO(8) symmetry in the Majorana representation of the problem. (2) The phenomena such as doping-induced insulator-superconductor transition, and new critical points induced by Dirac fermions, will be discussed time permitting.
(1) I. F. Herbut, Interactions and phase transitions on graphene's honeycomb lattice, Phys. Rev. Lett. vol. 97, 146401 (2006).
(2) I. F. Herbut, S. Mandal, SO(8) unification and the large-N theory of superconductor-insulator transition in two-dimensional Dirac fermions, Phys. Rev. B vol. 108, L161108 (2023).
第２１回 No. 21
講師 Speaker：Prof. Fabio Bagarello (U. Palermo, Italy)日時Date：２０２５年２月１３日（木）１４時３０分〜 / Thursday, 13th February 2025, 14:30 JST -
場所 Place: 東京大学生産技術研究所研究実験棟１（柏キャンパス）大会議室 The University of Tokyo, Institute of Industrial Science, Research and Testing Complex I (Kashiwa campus)Large Conference Room
演題Title：A brief introduction to non Hermitian Hamiltonians and on their dynamics: the role of ladder operators
要旨Abstract：
In my talk I will discuss some general aspects of quantum mechanics with non Hermitian Hamiltonians. In the first part I will introduce a general mathematical settings connected to this class of Hamiltonians. The level of this part is elementary. In the second part of my talk, I will describe more recent results. In particular:
- I will discuss few facts concerning the Heisenberg dynamics for non Hermitian Hamiltonians, from an algebraic point of view.
- I will propose a general procedure to find eigenstates and eigenvalues of a non self-adjoint Hamiltonians, based on the notion of abstract ladder operators.
- If I have time, I will also discuss some recent results on the role of distributions in quantum mechanics for pseudo-bosons. I will propose a new definition of multiplication of distributions, and discuss some applications, in connection with a generalized notion of biorthogonality.
The talk is based on the following works:
[1] F. Bagarello, Heisenberg dynamics for non self-adjoint Hamiltonians: symmetries and derivations, Math. Phys. Anal. Geom., 26, 1-15 (2023)
[2] F. Bagarello, Abstract ladder operators and their applications, J. Phys. A, 54, 445203 (2021)
[3] F. Bagarello, Abstract ladder operators for non self-adjoint Hamiltonians, with applications, Ann. of Phys., 468, 169727 (2024)
[4] F. Bagarello, F. Gargano, Bi-coherent states as generalized eigenstates of the position and the momentum operators, Z. Angew. Math. Phys., 73:119 (2022)
[5] F. Bagarello, Multiplication of distributions in a linear gain and loss system, Z. Angew. Math. Phys., 74:136 (2023)
[6] F. Bagarello, e-product of distributions, with applications, Z. Angew. Math. Phys. 76, 61 (2025)
[7] F. Bagarello, Pseudo-bosons and their coherent states, Springer (2022)
[8] C. M. Bender, PT Symmetry In Quantum and Classical Physics, World Scientific Publishing Europe Ltd., London (2019)