Non-Bloch band theory of non-Hermitian systems Kazuki Yokomizo RIKEN A non-Hermitian system is a nonequilibrium system which is described by a non-Hermitian Hamiltonian. Interestingly, some non-Hermitian tight-binding systems have the non-Hermitian skin effect which induces the localization of the bulk eigenstates [1]. Then, the non-Hermitian skin effect exhibits the difference between the energy bands under a periodic boundary condition and those under an open boundary condition. While the energy eigenvalues under a periodic boundary condition can be obtained from the conventional Bloch band theory, it is unclear how to calculate the energy eigenvalues under an open boundary condition. In this talk, I present the non-Bloch band theory which produces the energy eigenvalues of non-Hermitian crystals with an open boundary condition [2]. We show that in the limit of a large system size, the energy bands are calculated by the Brillouin zone unique to a non-Hermitian system. [1] S. Yao and Z. Wang, Phys. Rev. Lett. 121, 086803 (2018). [2] K. Yokomizo and S. Murakami, Phys. Rev. Lett. 123, 066404 (2019).