Integrable dissipative spin chains

Naoyuki Shibata (U. Tokyo)

We study the Lindblad equations for two spin chain models that can be mapped to integrable non-Hermitian models. The first model is a quantum compass chain with bulk dephasing. By vectorizing the density matrix, this model can be mapped to a non-Hermitian Kitaev model on a two-leg ladder, and hence is exactly solvable. The second is a quantum Ising chain with a particular form of bulk dissipation. With a similar mapping to that applied to the first model, it corresponds to a non-Hermitian Ashkin-Teller model, which can be further mapped to an XXZ spin chain with pure imaginary anisotropy $\Delta$. In both cases, we obtain exact results for the steady states and the Liouvillian gap (the inverse of the relaxation time) by exploiting the integrability of the systems.

References:
[1] N. Shibata and H. Katsura, Phys. Rev. B 99, 174303 (2019)
[2] N. Shibata and H. Katsura, Phys. Rev. B 99, 224432 (2019)