Dynamic Quantum Phase Transitions in Non-Hermitian Systems

Xiang Zhang, Kangyi Hu, Fuxiang Li

The authors generalize here the quantum metric framework to the \ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}} broken region, and investigate the nonadiabatic dynamics in non-Hermitian quantum systems. The authors demonstrate that the long-time average of the rate function can be used to characterize the \ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}} phase transitions. They also find that this framework can remove the accidental dynamical quantum phase transitions, and thus build a bridge between dynamical and equilibrium quantum phase transitions.

Longwen Zhou, Qinghai Wang, Hailong Wang +1 more

In closed quantum systems, dynamical phase transitions are identified by the nonanalytic behavior of the return probability as a function of time. In this work, we study the nonunitary dynamics following quenches across exceptional points in a non-Hermitian lattice realizable by optical resonators. Dynamical quantum phase transitions with topological signatures are found when an isolated exceptional point is crossed during the quench. A winding number defined by a real, noncyclic geometric phase is introduced, whose value features quantized jumps at critical times of these phase transitions and remains constant elsewhere, playing the role of a topological order parameter. This work provides a simple framework to study dynamical and topological quantum phase transitions in non-Hermitian systems.

Ralf Schützhold

Mingtao Xu, Wei Yi, De-Huan Cai

In quantum dynamics, the Loschmidt amplitude is analogous to the partition function in the canonical ensemble. Zeros in the partition function indicate a phase transition, while the presence of zeros in the Loschmidt amplitude indicates a dynamical quantum phase transition. Based on the classical-quantum correspondence, we demonstrate that the partition function of a classical Ising model is equivalent to the Loschmidt amplitude in non-Hermitian dynamics, thereby mapping an Ising model with variable system size to the non-Hermitian dynamics. It follows that the Yang-Lee zeros and the Yang-Lee edge singularity of the classical Ising model correspond to the critical times of the dynamic quantum phase transitions and the exceptional point of the non-Hermitian Hamiltonian, respectively. Our work reveals an inner connection between Yang-Lee zeros and non-Hermitian dynamics, offering a dynamic characterization of the former.