Field theory of non-Hermitian disordered systems
arXiv:2411.11878 · doi:10.1103/PhysRevB.111.054203
Abstract
The interplay between non-Hermiticity and disorder gives rise to unique universality classes of Anderson transitions. Here, we develop a field-theoretical description of non-Hermitian disordered systems based on fermionic replica nonlinear sigma models. We classify the target manifolds of the nonlinear sigma models across all the 38-fold symmetry classes of non-Hermitian systems and corroborate the correspondence of the universality classes of Anderson transitions between non-Hermitian systems and Hermitized systems with additional chiral symmetry. We apply the nonlinear sigma model framework to study the spectral properties of non-Hermitian random matrices with particle-hole symmetry. Furthermore, we demonstrate that the Anderson transition unique to nonreciprocal disordered systems in one dimension, including the Hatano-Nelson model, originates from the competition between the kinetic and topological terms in a one-dimensional nonlinear sigma model. We also discuss the critical phenomena of non-Hermitian disordered systems with symmetry and topology in higher dimensions.
25 pages, 2 figures, 7 tables
References in corpus (107)
- Classification of topological insulators and superconductors in three spatial dimensions
- Classification of topological quantum matter with symmetries
- Random-Matrix Theory of Quantum Transport
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Edge states and topological invariants of non-Hermitian systems
- Anderson Transitions
- Periodic table for topological insulators and superconductors
- Anderson localization of a non-interacting Bose-Einstein condensate
- Exceptional Topology of Non-Hermitian Systems
- Direct observation of Anderson localization of matter-waves in a controlled disorder
- 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
- Topological Origin of Non-Hermitian Skin Effects
- Nonlinear waves in -symmetric systems
- Anomalous edge state in a non-Hermitian lattice
- Non-Bloch Band Theory of Non-Hermitian Systems
- Correspondence between winding numbers and skin modes in non-hermitian systems
- Scaling Theory of the Integer Quantum Hall Effect
- Vortex Pinning and Non-Hermitian Quantum Mechanics
- The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
- Topological phase transition in non-Hermitian quasicrystals
- Non-Hermitian topological phenomena: A review
- Random Matrix Theory and Chiral Symmetry in QCD
- Demonstration of one-parameter scaling at the Dirac point in graphene
- Non-Hermitian Many-Body Localization
- Random-matrix theory of Majorana fermions and topological superconductors
- Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
- Topological delocalization of two-dimensional massless Dirac fermions
- Exact exponents for the spin quantum Hall transition
- Non-Hermitean Random Matrix Theory: method of hermitization
- Tenfold Way for Quadratic Lindbladians
- Topological Phases in Non-Hermitian Aubry-André-Harper Models
- Random Network Models and Quantum Phase Transitions in Two Dimensions
- Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
- Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos
- Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators
- Quantum criticality and minimal conductivity in graphene with long-range disorder
- Directed Quantum Chaos
- Non-Hermitean Localization and De-Localization
- Random Matrices close to Hermitian or unitary: overview of methods and results
- Critical exponent for the quantum Hall transition
- Skin effect and winding number in disordered non-Hermitian systems
- Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems
- Characteristic polynomials of random matrices
- 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
- Disordered weak and strong topological insulators
- Landauer conductance and twisted boundary conditions for Dirac fermions in two space dimensions
- Quantum Hall plateau transitions in disordered superconductors
- Universal spectra of random Lindblad operators
- Theory of directed localization in one dimension
- Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
- Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
- Theory of free fermions under random projective measurements
- Quantum criticality of quasi one-dimensional topological Anderson insulators
- Effect of Disorder in a Three-Dimensional Layered Chern Insulator
- Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
- Exceptional Topological Insulators
- Topological Field Theory of Non-Hermitian Systems
- Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
- Hierarchy of relaxation timescales in local random Liouvillians
- Spectral gaps and mid-gap states in random quantum master equations
- Quantum Disordered Systems with a Direction
- Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
- Nonlinear sigma models for monitored dynamics of free fermions
- Thermofield dynamics: Quantum Chaos versus Decoherence
- Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition
- Topology vs. Anderson localization: non-perturbative solutions in one dimension
- Lindbladian dissipation of strongly-correlated quantum matter
- Random Lindblad Dynamics
- Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems
- Symmetry Classification of Many-Body Lindbladians: Tenfold Way and Beyond
- Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos
- Lindbladian dynamics of the Sachdev-Ye-Kitaev model
- The integer quantum Hall plateau transition is a current algebra after all
- Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors
- Transfer matrix study of the Anderson transition in non-Hermitian systems
- Integrable sigma models with theta=pi
- Many-body quantum chaos and emergence of Ginibre ensemble
- Bulk-boundary correspondence in point-gap topological phases
- Spectral Properties of Disordered Interacting Non-Hermitian Systems
- Integer Quantum Magnon Hall Plateau-Plateau Transition in a Spin Ice Model
- Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble
- Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
- Keldysh Nonlinear Sigma Model for a Free-Fermion Gas under Continuous Measurements
- Replica treatment of non-Hermitian disordered Hamiltonians
- Level statistics of real eigenvalues in non-Hermitian systems
- Criticality of two-dimensional disordered Dirac fermions in the unitary class and universality of the integer quantum Hall transition
- Topological enhancement of non-normality in non-Hermitian skin effects
- Localization from sigma-model geodesics
- Scaling collapse of longitudinal conductance near the integer quantum Hall transition
- Non-Hermitian Hamiltonians Violate the Eigenstate Thermalization Hypothesis
- Anderson localization from the replica formalism
- Anisotropic Topological Anderson Transitions in Chiral Symmetry Classes
- Dynamical Transition due to Feedback-induced Skin Effect
- A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices
- Spectrum-wide quantum criticality at the surface of class AIII topological phases: An "energy stack" of integer quantum Hall plateau transitions
- Eigenvector Correlations Across the Localisation Transition in non-Hermitian Power-Law Banded Random Matrices
- Topological effect on the Anderson transition in chiral symmetry classes
- Field Theoretical Study of Disorder in Non-Hermitian Topological Models
- Universal hard-edge statistics of non-Hermitian random matrices
- Emergent Topology in Many-Body Dissipative Quantum Matter
Cited by in corpus (6)
- Universal non-Hermitian transport in disordered systems
- Correlations and Krylov spread for a non-Hermitian Hamiltonian: Ising chain with a complex-valued transverse magnetic field
- Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
- Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
- 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