Non-Hermitian Dynamics of Open Quantum Systems

Jacek Okołowicz, Marek Płoszajczak, I. Rotter

Li, Xiaogang, Kecheng Liu, Qi-Ming Ding

Non-Hermitian quantum systems exhibit unique properties and hold significant promise for diverse applications, yet their dynamical simulation poses a particular challenge due to intrinsic openness and non-unitary evolution. Here, we introduce a hybrid classical-quantum algorithm based on Quantum Monte Carlo (QMC) for simulating the dynamics of arbitrary time-dependent non-Hermitian systems. Notably, this approach constitutes a natural extension of the quantum imaginary-time evolution (QITE) algorithm. This algorithm combines the advantages of both classical and quantum computation and exhibits good applicability and adaptability, making it promising for simulating arbitrary non-Hermitian systems such as PT-symmetric systems, non-physical processes, and open quantum systems. To validate the algorithm, we applied it to the dynamic simulation of open quantum systems and achieved the desired results.

Yoshihiro Michishita, Robert Peters

Recently, it has become clear that non-Hermitian phenomena can be observed not only in open quantum systems experiencing gain and loss but also in equilibrium single-particle properties of strongly correlated systems. However, the circumstances and requirements for the emergence of non-Hermitian phenomena in each field are entirely different. While the implementation of postselection is a significant obstacle to observe the dynamics governed by a non-Hermitian Hamiltonian in open quantum systems, it is unnecessary in strongly correlated systems. Until now, a relation between both descriptions of non-Hermitian phenomena has not been revealed. In this Letter, we close this gap and demonstrate that the non-Hermitian Hamiltonians emerging in both fields are identical, and we clarify the conditions for the emergence of a non-Hermitian Hamiltonian in strongly correlated materials. Using this knowledge, we propose a method to analyze non-Hermitian properties without the necessity of postselection by studying specific response functions of open quantum systems and strongly correlated systems.

Keith H. Hughes

Carole Addis

Fei Song, Shunyu Yao, Zhong Wang

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. 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. These phenomena are beyond the effective non-Hermitian Hamiltonians; instead, they belong to the non-Hermitian physics of full-fledged open quantum dynamics.