Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions

Abstract

Non-Hermitian quasicrystal forms a unique class of matter with symmetry-breaking, localization and topological transitions induced by gain and loss or nonreciprocal effects. In this work, we introduce a non-Abelian generalization of the non-Hermitian quasicrystal, in which the interplay between non-Hermitian effects and non-Abelian quasiperiodic potentials create mobility edges and rich transitions among extended, critical and localized phases. These generic features are demonstrated by investigating three non-Abelian variants of the non-Hermitian Aubry-André-Harper model. A unified characterization is given to their spectrum, localization, entanglement and topological properties. Our findings thus add new members to the family of non-Hermitian quasicrystal and uncover unique physics that can be triggered by non-Abelian effects in non-Hermitian systems.

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References in corpus (46)

• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Topological phase transition in non-Hermitian quasicrystals
• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Reentrant Localization Transition in a Quasiperiodic Chain
• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Simulating non-Hermitian quasicrystals with single-photon quantum walks
• Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Non-Hermitian mobility edges in one-dimensional quasicrystals with parity-time symmetry
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Many-body localization in a non-Hermitian quasi-periodic system
• Localization and topological transitions in non-Hermitian quasiperiodic lattices
• Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy
• Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
• Fate of Majorana zero modes, critical states and non-conventional real-complex transition in non-Hermitian quasiperiodic lattices
• Dimerization induced mobility edges and multiple reentrant localization transitions in non-Hermitian quasicrystals
• Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-Andr{é}-Fibonacci chain
• Metal-Insulator Transition Revisited for Cold Atoms in Non-Abelian Gauge Potentials
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Anderson localization and topological phase transitions in non-Hermitian Aubry-André-Harper models with p-wave pairing
• Two-Dimensional Electron Gas with Cold Atoms in Non-Abelian Gauge Potentials
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Non-Hermitian spectra and Anderson localization
• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• Artificial non-Abelian lattice gauge fields for photons in the synthetic frequency dimension
• Quantum Entanglement of Non-Hermitian Quasicrystals
• Spectral Properties of Disordered Interacting Non-Hermitian Systems
• Non-Hermitian Maryland Model
• Entanglement Entropy of Non-Hermitian Free Fermions
• Localization, $\mathcal{P}\mathcal{T}$-Symmetry Breaking and Topological Transitions in non-Hermitian Quasicrystals
• Driving-induced multiple $\mathcal{P}\mathcal{T}$-symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals
• Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals
• Non-Hermitian quasicrystal in dimerized lattices
• Non-Abelian Generalizations of the Hofstadter model: Spin-orbit-coupled Butterfly Pairs
• Non-Hermitian pseudo mobility edge in a coupled chain system
• Entanglement, non-Hermiticity, and duality
• Polarization and entanglement spectrum in non-hermitian systems
• Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Non-Hermitian topological mobility edges and transport in photonic quantum walks
• Entanglement spectrum and entropy in Floquet topological matter
• Time-reversal Invariant SU(2) Hofstadter Problem in Three Dimensional Lattices

Cited by in corpus (15)

• Non-Hermitian Floquet Topological Matter -- A Review
• Synthetic non-Abelian gauge fields for non-Hermitian systems
• Entanglement phase transitions in non-Hermitian quasicrystals
• Non-Hermitian butterfly spectra in a family of quasiperiodic lattices
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal