Non-Hermitian Quantum Mechanics of Strongly Correlated Systems

祐一 中村

Yuichi Nakamura, Naomichi Hatano

Yuichi Nakamura, Naomichi Hatano

X. Z. Zhang, Peng Wang, Kun-Liang Zhang +2 more

In recent years, two independent research fields, i.e. non-Hermitian andstrongly correlated systems have been merged, forming an important researchfield in physics. The progress of relevant theories and experiments hasreshaped our understanding of matter. In this field, the research object isnot limited to the influence of non-Hermiticity on the energy spectrum andthe eigenstate properties of many-body systems. Researchers have paid more attentionto the manipulation of quantum states. It is universally received that the exceptional point is the most significant featurethat distinguishes non-Hermitian quantum mechanics from Hermitian quantum mechanics. In addition to the recent advances in non-Hermitian topological band theory and quantum sensing around the exceptional points, this paper concentrates on the non-Hermitian critical dynamical phenomenon and its application to the quantum many-body system. When the system has an exceptional point, an arbitrary initial state belonging to the coalescent subspace will be projected on the coalescent state. Based on the directionality of the evolved quantum state, this paper reviews our several representative researches in recent years, including local-field-induced dynamical magnetization, quantum phase transition in transverse field, Ising model at non-zero temperature, quantum mold casting in the center-environment system, as well as superconducting state preparation in the non-Hermitian strongly correlated system. We also focus on the new preparation methods and detection schemes of non-equilibrium quantum states related to exception points.

Fabian H. L. Eßler

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.