Transfer matrix study of the Anderson transition in non-Hermitian systems

Abstract

In this paper, we present in-depth transfer matrix analyses of the Anderson transition in three non-Hermitian (NH) systems, NH Anderson, U(1) and Peierls models, that belong to NH class AI${}^{†}$ or NH class A. We first argue a general validity of the transfer matrix analysis, and clarify the symmetry properties of the Lyapunov exponents, scattering ($S$) matrix and two-terminal conductance in these NH models. The unitarity of the $S$ matrix is violated in NH systems, where the two-terminal conductance can take arbitrarily large values. Nonetheless, we show that the transposition symmetry of a Hamiltonian leads to the symmetric nature of the $S$ matrix as well as the reciprocal symmetries of the Lyapunov exponents and conductance in certain ways in these NH models. Finite size scaling data are fitted by polynomial functions, from which we determine the critical exponent $\nu$ at different single-particle energies and system parameters of the NH models. We conclude that the critical exponents of the NH class AI${}^{†}$ and the NH class A are $\nu =1.19\pm 0.01$ and $\nu =1.00\pm 0.04$, respectively. In the NH models, a distribution of the two-terminal conductance is not Gaussian. Instead, it contains small fractions of huge conductance values, which come from rare-event states with huge transmissions amplified by on-site NH disorders. Nonetheless, a geometric mean of the conductance enables the finite-size scaling analysis. We show that the critical exponents obtained from the conductance analysis are consistent with those from the localization length in these three NH models.

arXiv comment18+2 pages

References in corpus (78)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Edge states and topological invariants of non-Hermitian systems
• Localization of interacting fermions at high temperature
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Analogs of quantum Hall effect edge states in photonic crystals
• Topological Origin of Non-Hermitian Skin Effects
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• PT-symmetric laser-absorber
• Non-Hermitian Chern bands
• Spawning rings of exceptional points out of Dirac cones
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• 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
• Localization of ultrasound in a three-dimensional elastic network
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• 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
• Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Non-Hermitian Topological Invariants in Real Space
• Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures
• Topological chiral magnonic edge mode in a magnonic crystal
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time 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
• Corrections to scaling at the Anderson transition
• Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem
• Chiral spin-wave edge modes in dipolar magnetic thin films
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos
• Non-Hermitian Kondo effect in ultracold alkaline-earth atoms
• Quantum noise and self-sustained radiation of PT-symmetric systems
• Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field
• Critical exponent for the Anderson transition in the three dimensional orthogonal universality class
• Topological Phase Transition driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics
• Nodal Arc in Disordered Dirac Fermions: Connection to Non-Hermitian Band Theory
• Non-Hermitian disorder in two-dimensional optical lattices
• Universality classes of non-Hermitian random matrices
• Nonunitary Scaling Theory of Non-Hermitian Localization
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Coherent perfect absorption of nonlinear matter waves
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Reconciling Conductance Fluctuations and the Scaling Theory of Localization
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Magnetic-field-driven localization of light in a cold-atom gas
• Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators
• Transport and spectral features in non-Hermitian open systems
• Critical Exponents for the Metal--Insulator Transition in Disordered Systems
• Critical Exponent of the Anderson Transition using Massively Parallel Supercomputing
• Spectral rigidity of non-Hermitian symmetric random matrices near Anderson transition
• From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
• Integer Quantum Magnon Hall Plateau-Plateau Transition in a Spin Ice Model
• Transfer Matrix Formulation of Scattering Theory in Two and Three Dimensions
• Scaling of the conductance distribution near the Anderson transition
• Light-controlled perfect absorption of light
• Compatibility of transport effects in non-Hermitian nonreciprocal systems
• Level statistics of extended states in random non-Hermitian Hamiltonians
• Localization transition for light scattering by cold atoms in an external magnetic field
• Anderson transitions in three-dimensional disordered systems with randomly varying magnetic flux
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes
• Universal routes to spontaneous PT-symmetry breaking in non-hermitian quantum systems
• Spectral singularities of odd-$PT$-symmetric potential
• $S$-matrix pole symmetries for non-Hermitian scattering Hamiltonians
• Berry curvature for coupled waves of magnons and electromagnetic waves

Cited by in corpus (34)

• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Non-Hermitian Topological Phases: Principles and Prospects
• Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Level statistics of real eigenvalues in non-Hermitian systems
• Anderson localization transitions in disordered non-Hermitian systems with exceptional points
• Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model
• Entanglement dynamics in the many-body Hatano-Nelson model
• Anderson localization in dissipative lattices
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Universal non-Hermitian transport in disordered systems
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Field theory of non-Hermitian disordered systems
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• Topological effect on the Anderson transition in chiral symmetry classes
• From scale-free to Anderson localization: a size-dependent transition
• Equivalence and superposition of real and imaginary quasiperiodicities
• Dynamical localization transition in the non-Hermitian lattice gauge theory
• Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes
• Universal hard-edge statistics of non-Hermitian random matrices
• Cavity quantum electrodynamics of photonic temporal crystals
• Localization of Lindbladian Fermions
• Non-Hermitian off-diagonal disordered optical lattices
• Entanglement dynamics of monitored noninteracting fermions on graphics processing units
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Many-Body Neural Network Wavefunction for a Non-Hermitian Ising Chain
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors
• Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI${}^{†}$ and AII${}^{†}$
• Controlled Zeno-Induced Localization of Free Fermions in a Quasiperiodic Chain