A Classification of Non-Hermitian Random Matrices

Abstract

We present a classification of non-hermitian random matrices based on implementing commuting discrete symmetries. It contains 38 classes. This generalizes the classification of hermitian random matrices due to Altland-Zirnbauer and it also extends the Ginibre ensembles of non-hermitian matrices.

8 pages, contribution to the proceedings of the NATO Advanced Research Workshop on Statistical Field Theories, Como (Italy), 18-23 June 2001. Compared to our 2001 version, we corrected two misprints in one table that in the previous version led us to miscount the number of classes as 43 whereas it should have been 38. Explicit details of the classification are unchanged

References in corpus (1)

• A Classification of random Dirac fermions

Cited by in corpus (50)

• Symmetry and Topology in Non-Hermitian Physics
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Non-Hermitian topological phenomena: A review
• Symmetry-protected nodal phases in non-Hermitian systems
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Tenfold Way for Quadratic Lindbladians
• Non-Hermitian band topology and skin modes in active elastic media
• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Nonunitary Scaling Theory of Non-Hermitian Localization
• Topological symmetry classes for non-Hermitian models and connections to the bosonic Bogoliubov-de Gennes equation
• 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
• Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
• Realizing exceptional points of any order in the presence of symmetry
• The Complex Laguerre Symplectic Ensemble of Non-Hermitian Matrices
• Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings
• Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems
• Random matrices beyond the Cartan classification
• Integrable nonunitary open quantum circuits
• Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Experimental Simulation of Symmetry-Protected Higher-Order Exceptional Points with Single Photons
• Products of Independent Gaussian Random Matrices
• Squaring the fermion: The threefold way and the fate of zero modes
• Hermitian and Non-Hermitian Topology from Photon-Mediated Interactions
• Symmetry indicator in non-Hermitian systems
• Polarization and entanglement spectrum in non-hermitian systems
• Making topologically trivial non-Hermitian systems nontrivial via gauge fields
• New universality classes of the non-Hermitian Dirac operator in QCD-like theories
• Microscopic universality of complex matrix model correlation functions at weak non-Hermiticity
• Quantum Electrodynamics of Non-Hermitian Dirac Fermions
• $Q$-Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Yukawa-Lorentz Symmetry in Non-Hermitian Dirac Materials
• Non-Hermitian extensions of Wishart random matrix ensembles
• Two-dimensional non-Hermitian topological phases induced by asymmetric hopping in a one-dimensional superlattice
• Non-Hermitian BCS-BEC crossover of Dirac fermions
• A geometrical triumvirate of real random matrices
• Replica Symmetry Breaking for the Integrable Two-Site Sachdev-Ye-Kitaev Model
• Universal Stochastic Equations of Monitored Quantum Dynamics
• $\mathcal{P}\mathcal{T}$ symmetry-protected exceptional cones and analogue Hawking radiation
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice
• Yukawa-Lorentz symmetry of interacting non-Hermitian birefringent Dirac fermions
• Asymmetric random matrices: What do we need them for?
• Symmetry classes of classical stochastic processes
• CDT as a scaling limit of matrix models
• Intrinsic non-Hermitian topological phases
• Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI${}^{†}$ and AII${}^{†}$
• Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz operators and singular values