Non-Hermitian skin effect and chiral damping in open quantum systems*

One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely, that the eigenstates are exponentially localized at the boundary of the system. The non-Hermitian skin effect plays a crucial role in the non-Hermitian topology and bulk-boundary correspondence. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians, while long-time dynamics calls for the Lindblad master equations, in which the Liouvillian superoperators generate time evolution. In this Letter, we find that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and uncover its unexpected physical consequences. It is shown that the non-Hermitian skin effect dramatically shapes the long-time dynamics, such that the damping in a class of open quantum systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. Moreover, the non-Hermitian skin effect and non-Bloch bands cause a chiral damping with a sharp wave front.
References:
[1] Fei Song, Shunyu Yao, Zhong Wang, PRL. 123, 170401 (2019)
[2] Shunyu Yao, Fei Song, Zhong Wang, PRL. 121, 136802 (2018)
[3] Shunyu Yao, Zhong Wang, PRL. 121, 086803 (2018)