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arXiv:2304.04588 · Physical Review Research

Composite quantum phases in non-Hermitian systems

Yuchen Guo, Ruohan Shen, Shuo Yang

Published Sep 12, 2023• 4 citations
arXivHTMLPDF

Abstract

Non-Hermitian systems have attracted considerable interest in recent years owing to their unique topological properties that are absent in Hermitian systems. While such properties have been thoroughly characterized in free fermion models, they remain an open question for interacting bosonic systems. In this work, we present a precise definition of quantum phases for non-Hermitian systems and propose a family of phases referred to as composite quantum phases. We demonstrate the existence of these phases in a one-dimensional spin-1 system and show their robustness against perturbations through numerical simulations. Furthermore, we investigate the phase diagram of our model, indicating the extensive presence of these phases in non-Hermitian systems. Our work establishes an alternate framework for studying and constructing quantum phases in non-Hermitian interacting systems, revealing exciting possibilities beyond the single-particle picture.

DOI
10.1103/physrevresearch.5.033181

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Non-Hermitian systems have attracted considerable interest in recent years owing to their unique topological properties that are absent in Hermitian systems. While such properties have been thoroughly characterized in free fermion models, they remain an open question for interacting bosonic systems. In this work, we present a precise definition of quantum phases for non-Hermitian systems and propose a family of phases referred to as composite quantum phases. We demonstrate the existence of these phases in a one-dimensional spin-1 system and show their robustness against perturbations through numerical simulations. Furthermore, we investigate the phase diagram of our model, indicating the extensive presence of these phases in non-Hermitian systems. Our work establishes an alternate framework for studying and constructing quantum phases in non-Hermitian interacting systems, revealing exciting possibilities beyond the single-particle picture.
Abstract The dynamical and topological properties of non-Hermitian systems have attracted great attention in recent years. In this work, we establish an intrinsic connection between two classes of intriguing phenomena—topological phases and dynamical quantum phase transitions (DQPTs)—in non-Hermitian systems. Focusing on one-dimensional models with chiral symmetry, we find DQPTs following the quench from a trivial to a non-Hermitian topological phase. Moreover, the critical momenta and critical time of the DQPTs are found to be directly related to the topological invariants of the non-Hermitian system. We further demonstrate our theory in three prototypical non-Hermitian lattice models, the lossy Kitaev chain (LKC), the LKC with next-nearest-neighbor hoppings, and the nonreciprocal Su–Schrieffer–Heeger model. Finally, we suggest a proposal to experimentally verify the found connection by a nitrogen-vacancy center in diamond.
Abstract This topical review article reports rapid progress on the generalization and application of entanglement in non-Hermitian free-fermion quantum systems. We begin by examining the realization of non-Hermitian quantum systems through the Lindblad master equation, alongside a review of typical non-Hermitian free-fermion systems that exhibit unique features. A pedagogical discussion is provided on the relationship between entanglement quantities and the correlation matrix in Hermitian systems. Building on this foundation, we focus on how entanglement concepts are extended to non-Hermitian systems from their Hermitian free-fermion counterparts, with a review of the general properties that emerge. Finally, we highlight various concrete studies, demonstrating that entanglement entropy remains a powerful diagnostic tool for characterizing non-Hermitian physics. The entanglement spectrum also reflects the topological characteristics of non-Hermitian topological systems, while unique non-Hermitian entanglement behaviors are also discussed. The review is concluded with several future directions. Through this review, we hope to provide a useful guide for researchers who are interested in entanglement in non-Hermitian quantum systems.
Recent years have seen a growing interest in topological phases beyond the standard paradigm of gapped isolated systems. One recent direction is to explore topological features in non-Hermitian systems that are commonly used as effective descriptions of open systems. Another direction explores the fate of topology at critical points, where the bulk gap collapses. One interesting observation is that both systems, though very different, share certain topological features. For instance, both systems can host half-integer quantized winding numbers and have very similar entanglement spectra. Here we make this similarity explicit by showing the equivalence of topological invariants in critical systems with non-Hermitian point-gap phases, in the presence of sublattice symmetry. Also, the corresponding entanglement spectra show the same topological features. This correspondence may carry over to other features and even be helpful to deepen our understanding of non-Hermitian systems using our knowledge of critical systems and vice versa.
We study quantum (T = 0) phases of strongly-correlated matter, and their possible implementation in a quantum simulator. We focus on the non-perturbative regimes of 1D spin-boson models. As a reference physical system we consider trapped-ion chains. We realize complex many-body states, such as a ground state exhibiting magnetic frustration, a lattice gauge theory, and a topological insulator. The exquisite control over these phases offered by a quantum simulator opens up exciting possibilities for exploring the exotic phenomena emerging in these systems, such as enhanced fluctuations and correlations. We address the non-perturbative regimes of the phase diagrams by means of mean-field theories and the numerical algorithm DMRG. We have established the universality class of the continuous transition in the spin-boson chain, the existence of a first order phase transition when the system is endowed with a gauge symmetry, and the possibility of probing topological states of matter in these systems. Our results show that some of the most exotic phases of quantum matter can be readily realized in trapped-ion quantum simulators. This offers the possibility of exploring these physical models beyond their original realm of applicability, which may provide us with new insights on both theoretical and applied fields of physics, ranging from high-energy processes to low-energy cooperative phenomena.
We introduce unitary quantum phase operators for material particles. We carry out a model study on quantum phases of interacting bosons in a symmetric double-well potential in terms of unitary and commonly-used non-unitary phase operators and compare the results for different number of bosons. We find that the results for unitary quantum phase operators are significantly different from those for non-unitary ones especially in the case of low number of bosons. We introduce unitary operators corresponding to the quantum phase-difference between two single-particle states of fermions. As an application of fermionic phase operators, we study a simple model of a pair of interacting two-component fermions in a symmetric double-well potential. We also investigate quantum phase and number fluctuations to ascertain number-phase uncertainty in terms of unitary phase operators.
Describing open quantum systems in terms of effective non-Hermitian Hamiltonians gives rise to nonunitary time evolution. In this paper we study the impact of nonunitary dynamics on the emergent hydrodynamics in quantum systems with a global conservation law. To this end we demonstrate how linear-response correlation functions can be generalized and interpreted in the case of non-Hermitian systems. Moreover we show that dynamical quantum typicality provides an efficient numerical approach to evaluate such correlation functions, even though the nonunitary dynamics leads to subtleties that are absent in the Hermitian case. As a point of reference for our analysis, we consider the Hermitian spin-1/21/21/2 XXZ chain, whose high-temperature transport properties have been characterized extensively in recent years. Here we explore the resulting hydrodynamics for different non-Hermitian perturbations of the XXZ chain. We also discuss the role of integrability by studying the complex energy-level statistics of the non-Hermitian quantum models.