Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling

Abstract

We investigate a uniformly coupled non-Hermitian system with asymmetric coupling amplitude. The asymmetric coupling equals to a symmetric coupling threaded by an imaginary gauge field. In a closed configuration, the imaginary gauge field leads to an imaginary magnetic flux, which induces a non-Hermitian phase transition. For an open boundary, the imaginary gauge field results in an eigenstate localization. The eigenstates under Dirac and biorthogonal norms and the scaling laws are quantitatively investigated to show the affect of asymmetric coupling induced one-way amplification. However, the imaginary magnetic flux does not inevitably induce the non-Hermitian phase transition for systems without translation invariance, this is elucidated from the non-Hermitian phase transition in the non-Hermitian ring with a single coupling defect. Our findings provide insights into the non-Hermitian phase transition and one-way localization.

10 pages, 5 figures, to appear in Phys. Rev. A

References in corpus (96)

• Making Sense of Non-Hermitian Hamiltonians
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Edge states and topological invariants of non-Hermitian systems
• Topological phases of non-Hermitian systems
• The physics of exceptional points
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Band Theory for Non-Hermitian Hamiltonians
• Coherent Perfect Absorbers: Time-reversed Lasers
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Topological energy transfer in an optomechanical system with exceptional points
• Visualization of Branch Points in PT-Symmetric Waveguides
• Non-Hermitian Chern bands
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Spawning rings of exceptional points out of Dirac cones
• Anatomy of skin modes and topology in non-Hermitian systems
• 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
• PT-Symmetric Phonon Laser
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Complex Edge-State Phase Transitions in 1D Topological Laser Arrays
• Topology by Dissipation in Atomic Quantum Wires
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Edge states and topological phases in non-Hermitian systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Anti-Parity-Time Symmetric Optics via Flying Atoms
• Metrology with $\mathcal{P}\mathcal{T}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{P}\mathcal{T}$-phase transition
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Topological Hybrid Silicon Microlasers
• Topologically protected midgap states in complex photonic lattices
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• New topological invariants in non-Hermitian systems
• Optical Resonator Analog of a Two-Dimensional Topological Insulator
• Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices
• PT-Symmetric Electronics
• Photonic Topological Insulating Phase Induced Solely by Gain and Loss
• Topological states of non-Hermitian systems
• Robust light transport in non-Hermitian photonic lattices
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Encircling an Exceptional Point
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Symmetry-protected nodal phases in non-Hermitian systems
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Anomalous helical edge states in a non-Hermitian Chern insulator
• High-order exceptional points in optomechanics
• Non-Hermitian Hopf-Link Exceptional Line Semimetals
• Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point
• Parity-time-symmetric topological superconductor
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Exceptional Links and Twisted Fermi Ribbons in non-Hermitian Systems
• Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
• Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
• Topological phases and edge states in a non-Hermitian trimerized optical lattice
• Edge states in trimer lattices
• Knotted Non-Hermitian Metals
• Dynamical quantum phase transitions in non-Hermitian lattices
• Topological phase in a non-Hermitian PT symmetric system
• Topological invariants and phase diagrams for one-dimensional two-band non-Hermitian systems without chiral symmetry
• Exceptional contours and band structure design in parity-time symmetric photonic crystals
• Incident Direction Independent Wave Propagation and Unidirectional Lasing
• Topological classification of non-Hermitian systems with reflection symmetry
• Topological symmetry classes for non-Hermitian models and connections to the bosonic Bogoliubov-de Gennes equation
• Edge states at the interface of non-Hermitian systems
• Exceptional points in topological edge spectrum of PT symmetric domain walls
• Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals
• Su-Schrieffer-Heeger chain with one pair of PT-symmetric defects
• Majorana Edge Modes with Gain and Loss
• Theory of superconductivity with non-Hermitian and parity-time reversal symmetric cooper pairing symmetry
• Transmission Nonreciprocity in a Mutually Coupled Circulating Structure
• Effects of Non-Hermiticity on Su-Schrieffer-Heeger Defect States
• Dynamical Phonon Laser in Coupled Active-Passive Microresonators
• Stabilizing Non-Hermitian Systems by Periodic Driving
• Degrees and signatures of broken PT-symmetry in (non-uniform) lattices
• High order exceptional points in ultracold Bose gases
• Non-Hermitian lattices with a flat band and polynomial power increase
• Topological phonon polaritons in one-dimensional non-Hermitian nanoparticle chains
• Topological photonic states in one-dimensional dimerized ultracold atomic chains
• Topological multiband photonic superlattices
• Parity-time symmetric coupled asymmetric dimers
• Exceptional points for parameter estimation in open quantum systems: Analysis of the Bloch equations
• Stable topological edge states in a non-Hermitian four-band model
• Exceptional Points in Two Dissimilar Coupled Diode Lasers
• Stability Through Asymmetry: Modulationally Stable Nonlinear Supermodes of Asymmetric non-Hermitian Optical Couplers
• Nodal Manifolds Bounded by Exceptional Points on Non-Hermitian Honeycomb Lattices and Electrical-Circuit Realizations
• Wave emission and absorption at spectral singularities
• Spontaneously Broken Particle-Hole Symmetry in Photonic Graphene with Gain and Loss
• Anomalous minimum and scaling behavior of localization length near an isolated flat band

Cited by in corpus (21)

• Non-Hermitian Topology and Exceptional-Point Geometries
• Active topological photonics
• Topological Anderson insulators in two-dimensional non-Hermitian disordered systems
• Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-Andr{é}-Fibonacci chain
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Nonlinear non-Hermitian skin effect
• Inversion symmetric non-Hermitian Chern insulator
• Topology in non-Hermitian Chern insulators with skin effect
• Chiral current circulation and $\mathcal{P}\mathcal{T}$ symmetry in a trimer of oscillators
• Non-Hermitian edge burst without skin localizations
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Work statistics in non-Hermitian evolutions with Hermitian endpoints
• From scale-free to Anderson localization: a size-dependent transition
• Eigenstate clustering around exceptional points
• Quasi-stationary solutions in non-Hermitian systems
• Extended unitarity and absence of skin effect in periodically driven systems
• Boundary-driven many-body phase transitions in a non-Hermitian disordered fermionic chain
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Semi-localization transition driven by a single asymmetrical tunneling
• Topology and criticality in non-Hermitian multimodal optical resonators through engineered losses
• Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping