Exceptional band touching for strongly correlated systems in equilibrium

Abstract

Quasi-particles described by Green's functions of equilibrium systems exhibit non-Hermitian topological phenomena because of their finite lifetime. This non-Hermitian perspective on equilibrium systems provides new insights into correlated systems and attracts much interest because of its potential to solve open questions in correlated compounds. In this paper, we provide a concise review of the non-Hermitian topological band structures for quantum many-body systems in equilibrium as well as their classification.

25 pages, 11 figures. Submitted to special section of Progress of Theoretical and Experimental Physics as an invited article

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Cited by in corpus (43)

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• Symmetry-protected multifold exceptional points and their topological characterization
• Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems
• Exceptional Spin Liquids from Couplings to the Environment
• Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
• Non-Hermitian Floquet Topological Matter -- A Review
• Non-Hermitian Mott Skin Effect
• Non-Hermitian topological phases and dynamical quantum phase transitions: A generic connection
• Phase Transitions and Generalized Biorthogonal Polarization in Non-Hermitian Systems
• Bulk-boundary correspondence in point-gap topological phases
• Non-Hermitian topology in monitored quantum circuits
• Square-root topological phase with time-reversal and particle-hole symmetry
• Universal platform of point-gap topological phases from topological materials
• R-DMFT study of a non-Hermitian skin effect for correlated systems: analysis based on a pseudo-spectrum
• Fourth-Order Exceptional Points in Correlated Quantum Many-Body Systems
• Exceptional points in the one-dimensional Hubbard model
• Topological enhancement of non-normality in non-Hermitian skin effects
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
• Bulk-edge correspondence for nonlinear eigenvalue problems
• Degeneracies and symmetry breaking in pseudo-Hermitian matrices
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder
• Symmetry protected exceptional points of interacting fermions
• Exceptional degeneracies in non-Hermitian Rashba semiconductors
• Correlation effects on non-Hermitian point-gap topology in zero dimension: reduction of topological classification
• Exceptional dynamics of interacting spin liquids
• Exceptional points in Fermi liquids with quadrupolar interactions
• Dynamically Induced Exceptional Phases in Quenched Interacting Semimetals
• Topological band theory of a generalized eigenvalue problem with Hermitian matrices: Symmetry-protected exceptional rings with emergent symmetry
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• Surface exceptional points in a topological Kondo insulator
• $\mathcal{P}\mathcal{T}$ symmetry-protected exceptional cones and analogue Hawking radiation
• A symmetry-protected exceptional ring in a photonic crystal with negative index media
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• Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities
• Spontaneous Formation of Exceptional Points at the Onset of Magnetism
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• Winding Topology of Multifold Exceptional Points
• Bulk--Boundary Correspondence and Boundary Zero Modes in a Non-Hermitian Kitaev Chain Model
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
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• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping