Level statistics of extended states in random non-Hermitian Hamiltonians

Abstract

Absence of level repulsion between extended states in random non-Hermitian systems is demonstrated. As a result, the general Wigner-Dyson distributions of level spacing of diffusive metals in the usual Hermitian systems is replaced by the Poisson distribution for quasiparticle level spacing of non-Hermitian disordered metals in the thermodynamic limit of infinite system size. This is a very surprising result because Poisson statistics is universally true for the Anderson insulators where energy eigenstates do not overlap with each other so that energy levels are independent from each other.For disordered metals where different eigenstates overlap with each other, one should expect different levels trying to stay away from each other so that the Poisson distribution should not apply there. Our results show that the larger non-Hermitian energy (dissipation) can invalidate level repulsion principle that holds dearly in quantum mechanics. Thus, our theory provides a unified picture for recent discovery of so called "level attraction" in various systems. It provides also a theoretical basis for manipulating energy levels.

arXiv comment10 pages, 8 figures

References in corpus (49)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Topological Photonics
• Edge states and topological invariants of non-Hermitian systems
• New Perspectives for Rashba Spin-Orbit Coupling
• Anderson Transitions
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• Topological Band Theory for Non-Hermitian Hamiltonians
• Anomalous edge state in a non-Hermitian lattice
• Loss-induced suppression and revival of lasing
• Visualization of Branch Points in PT-Symmetric Waveguides
• Non-Hermitian Chern bands
• Spawning rings of exceptional points out of Dirac cones
• 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
• Observation of the Magnon Hall Effect
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• Topology by Dissipation in Atomic Quantum Wires
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Edge states and topological phases in non-Hermitian systems
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Level Attraction Due to Dissipative Magnon-Photon Coupling
• PT symmetry and spontaneous symmetry breaking in a microwave billiard
• Non-Hermitian Many-Body Localization
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Topological invariance and global Berry phase in non-Hermitian systems
• Heralded magnetism in non-Hermitian atomic systems
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Entanglement and spin squeezing in non-Hermitian phase transitions
• Abnormal anti-crossing effect in photon-magnon coupling
• Nodal Arc in Disordered Dirac Fermions: Connection to Non-Hermitian Band Theory
• Anderson localization and the quantum phase diagram of three dimensional disordered Dirac semimetals
• Hall Conductance of a Non-Hermitian Chern Insulator
• Non-Hermitian disorder in two-dimensional optical lattices
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Topological quantum wires with balanced gain and loss
• Exceptional points in topological edge spectrum of PT symmetric domain walls
• Winding Numbers, Complex Currents, and Non-Hermitian Localization
• Control of the magnon-photon level attraction in a planar cavity
• Topological phases in Kitaev chain with imbalanced pairing
• Loss of Hall Conductivity Quantization in a Non-Hermitian Quantum Anomalous Hall Insulator
• Control of the Coupling Strength and the Linewidth of a Cavity-Magnon Polariton
• Microscopic mechanism of level attraction
• Antiferromagnetism emerging in a ferromagnet with gain
• Edge states in a two-dimensional honeycomb lattice of massive magnetic skyrmions
• Anderson transition of cold atoms with synthetic spin-orbit coupling in two-dimensional speckle potentials
• Nearest level spacing statistics in open chaotic systems: a generalization of the Wigner Surmise
• Unusual Metal to Marginal-Metal Transition in Two-Dimensional Ferromagnetic Electron Gases
• Non-Quantized Edge Channel Conductance and Zero Conductance Fluctuation in Non-Hermitian Chern Insulators

Cited by in corpus (21)

• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems
• Transfer matrix study of the Anderson transition in non-Hermitian systems
• Real space topological invariant and higher-order topological Anderson insulator in two-dimensional non-Hermitian systems
• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• Bulk-Bulk Correspondence in Disordered Non-Hermitian Systems
• Non-Hermitian Hamiltonian Deformations in Quantum Mechanics
• The Global Phase Diagram of disordered Higher-order Weyl Semimetals
• Level statistics of real eigenvalues in non-Hermitian systems
• Anderson localization transitions in disordered non-Hermitian systems with exceptional points
• Universality classes of the Anderson transition in three-dimensional symmetry classes AIII, BDI, C, D and CI
• Anderson Delocalization in Strongly Coupled Disordered Non-Hermitian Chains
• Quantum Chaos and Coherence: Random Parametric Quantum Channels
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• Hermitian chiral boundary states in non-Hermitian topological insulators
• Critical and non critical non-Hermitian topological phase transitions in one dimensional chains
• Universal hard-edge statistics of non-Hermitian random matrices
• Chiral Hinge Transport in Disordered Non-Hermitian Second-Order Topological Insulators
• Linear level repulsions near exceptional points of non-Hermitian systems
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors