Localization and topological transitions in non-Hermitian quasiperiodic lattices

Abstract

We investigate the localization and topological transitions in a one-dimensional (interacting) non-Hermitian quasiperiodic lattice, which is described by a generalized Aubry-André-Harper model with irrational modulations in the off-diagonal hopping and on-site potential and with non-Hermiticities from the nonreciprocal hopping and complex potential phase. For noninteracting cases, we reveal that the nonreciprocal hopping (the complex potential phase) can enlarge the delocalization (localization) region in the phase diagrams spanned by two quasiperiodical modulation strengths. We show that the localization transition are always accompanied by a topological phase transition characterized the winding numbers of eigenenergies in three different non-Hermitian cases. Moreover, we find that a real-complex eigenenergy transition in the energy spectrum coincides with (occurs before) these two phase transitions in the nonreciprocal (complex potential) case, while the real-complex transition is absent under the coexistence of the two non-Hermiticities. For interacting spinless fermions, we demonstrate that the extended phase and the many-body localized phase can be identified by the entanglement entropy of eigenstates and the level statistics of complex eigenenergies. By making the critical scaling analysis, we further show that the many-body localization transition coincides with the real-complex transition and occurs before the topological transition in the nonreciprocal case, which are absent in the complex phase case.

arXiv comment10 pages, 8 figures; accepted by PRA

References in corpus (83)

• Topological insulators and superconductors
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Edge states and topological invariants of non-Hermitian systems
• Anderson localization of a non-interacting Bose-Einstein condensate
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Topological States and Adiabatic Pumping in Quasicrystals
• Anomalous edge state in a non-Hermitian lattice
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Non-Hermitian Chern bands
• Non-Hermitian Boundary Modes
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Edge states and topological phases in non-Hermitian systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Non-Hermitian Topological Invariants in Real Space
• Topological Transition in a Non-Hermitian Quantum Walk
• Direct observation of a localization transition in quasi-periodic photonic lattices
• Topological phase transition in non-Hermitian quasicrystals
• Coupling Identical 1D Many-Body Localized Systems
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• New topological invariants in non-Hermitian systems
• Edge states and topological phases in one-dimensional optical superlattices
• Topological quantum matter with cold atoms
• Non-Hermitian Many-Body Localization
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
• Signatures of Many-Body Localization in a Controlled Open Quantum System
• Robust light transport in non-Hermitian photonic lattices
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Topological invariance and global Berry phase in non-Hermitian systems
• Observation of many-body localization in a one-dimensional system with single-particle mobility edge
• Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction
• Anderson localization in Bose-Einstein condensates
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Heralded magnetism in non-Hermitian atomic systems
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper Model
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field
• Entanglement and spin squeezing in non-Hermitian phase transitions
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
• Topological phases and edge states in a non-Hermitian trimerized optical lattice
• Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems
• Dynamical quantum phase transitions in non-Hermitian lattices
• Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states
• Non-Hermitian Topological Anderson Insulators
• Topological invariants and phase diagrams for one-dimensional two-band non-Hermitian systems without chiral symmetry
• Hall Conductance of a Non-Hermitian Chern Insulator
• Non-Hermitian disorder in two-dimensional optical lattices
• Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
• Topological classification of non-Hermitian systems with reflection symmetry
• Many-body localization in a non-Hermitian quasi-periodic system
• Edge states at the interface of non-Hermitian systems
• Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices
• Correlated Fermions in a one-dimensional quasiperiodic potential
• Many-body critical phase: extended and nonthermal
• Non-Hermitian fractional quantum Hall states
• Topological equivalence of crystal and quasicrystal band structures
• Topological Anderson insulators in two-dimensional non-Hermitian disordered systems
• Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices
• The non-Hermitian Swanson model with a time-dependent metric
• Interacting fermions in self-similar potentials
• Stable topological edge states in a non-Hermitian four-band model
• Dynamical topological invariant for non-Hermitian Rice-Mele model
• Topological spin excitations in Harper-Heisenberg spin chains
• Exceptional points and Bloch oscillations in non-Hermitian lattices with unidirectional hopping
• Statistically related many-body localization in the one-dimensional anyon Hubbard model
• Two-dimensional non-Hermitian topological phases induced by asymmetric hopping in a one-dimensional superlattice

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