Tenfold Way for Quadratic Lindbladians

Abstract

We uncover a topological classification applicable to open fermionic systems governed by a general class of Lindblad master equations. These `quadratic Lindbladians' can be captured by a non-Hermitian single-particle matrix which describes internal dynamics as well as system-environment coupling. We show that this matrix must belong to one of ten non-Hermitian Bernard-LeClair symmetry classes which reduce to the Altland-Zirnbauer classes in the closed limit. The Lindblad spectrum admits a topological classification, which we show results in gapless edge excitations with finite lifetimes. Unlike previous studies of purely Hamiltonian or purely dissipative evolution, these topological edge modes are unconnected to the form of the steady state. We provide one-dimensional examples where the addition of dissipators can either preserve or destroy the closed classification of a model, highlighting the sensitivity of topological properties to details of the system-environment coupling.

arXiv comment5 + 3 pages, 4 figures

References in corpus (38)

• Topological Insulators
• Topological insulators and superconductors
• Anyons in an exactly solved model and beyond
• Unpaired Majorana fermions in quantum wires
• Classification of topological quantum matter with symmetries
• New directions in the pursuit of Majorana fermions in solid state systems
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Symmetry and Topology in Non-Hermitian Physics
• Topology by Dissipation in Atomic Quantum Wires
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Edge states and topological phases in non-Hermitian systems
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Periodic Table for Floquet Topological Insulators
• Topology by dissipation
• Classification of Interacting Topological Floquet Phases in One Dimension
• Classification of topological phases in periodically driven interacting systems
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Spectral theorem for the Lindblad equation for quadratic open fermionic systems
• Failure of protection of Majorana based qubits against decoherence
• Geometry and response of Lindbladians
• Topology of density matrices
• Universal spectra of random Lindblad operators
• Topological symmetry classes for non-Hermitian models and connections to the bosonic Bogoliubov-de Gennes equation
• Probing the topology of density matrices
• Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model
• Topological classification of defects in non-Hermitian systems
• Topology of one dimensional quantum systems out of equilibrium
• Spectral gaps and mid-gap states in random quantum master equations
• A Classification of Non-Hermitian Random Matrices
• Classification of topological insulators and superconductors out of equilibrium
• Dynamical signatures of topological order in the driven-dissipative Kitaev chain
• Stretched exponential decay of Majorana edge modes in many-body localized Kitaev chains under dissipation
• Selective Population of Edge States in a 2D Topological Band System
• Dissipation-induced topological insulators: A no-go theorem and a recipe
• Dynamical Response Theory for Driven-Dissipative Quantum Systems

Cited by in corpus (139)

• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Non-Hermitian topological phenomena: A review
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Fermion doubling theorems in 2D non-Hermitian systems for Fermi points and exceptional points
• Symmetry breaking and error correction in open quantum systems
• Many-body topology of non-Hermitian systems
• Helical damping and anomalous critical non-Hermitian skin effect
• Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
• Non-equilibrium stationary states of quantum non-Hermitian lattice models
• Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Symmetry classes of open fermionic quantum matter
• Liouvillian Skin Effect in an Exactly Solvable Model
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Nonlinear sigma models for monitored dynamics of free fermions
• Lindbladian dissipation of strongly-correlated quantum matter
• Universality in driven open quantum matter
• Non-Hermitian skin effect beyond the tight-binding models
• Symmetry Classification of Many-Body Lindbladians: Tenfold Way and Beyond
• Emergence of PT-symmetry breaking in open quantum systems
• Spectral and Steady-State Properties of Random Liouvillians
• Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
• Non-Hermitian Mott Skin Effect
• Field Theory of Many-Body Lindbladian Dynamics
• Dissipative Topological Phase Transition with Strong System-Environment Coupling
• Integrable nonunitary open quantum circuits
• Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems
• Lindblad master equation approach to the topological phase transition in the disordered Su-Schrieffer-Heeger model
• Fragility of Time-Reversal Symmetry Protected Topological Phases
• Disorder-driven Phase Transitions of Second-order Non-Hermitian Skin Effects
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Theoretical Prediction of Non-Hermitian Skin Effect in Ultracold Atom Systems
• Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification
• Entanglement Spectrum Crossings Reveal non-Hermitian Dynamical Topology
• Non-Hermitian topology in monitored quantum circuits
• Continuous Dissipative Phase Transitions without Symmetry Breaking
• Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• $\mathcal{P}\mathcal{T}$ phase transition in open quantum systems with Lindblad dynamics
• R-DMFT study of a non-Hermitian skin effect for correlated systems: analysis based on a pseudo-spectrum
• Topological phases protected by shifted sublattice symmetry in dissipative quantum systems
• Universal platform of point-gap topological phases from topological materials
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations
• Quantum-Squeezing-Induced Point-Gap Topology and Skin Effect
• Unraveling the topology of dissipative quantum systems
• Non-Hermitian many-body topological excitations in interacting quantum dots
• Real spectra in non-Hermitian topological insulators
• Level statistics of real eigenvalues in non-Hermitian systems
• Renyi Entropy Dynamics and Lindblad Spectrum for Open Quantum System
• Topological enhancement of non-normality in non-Hermitian skin effects
• Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss
• The fate of high winding number topological phases in the disordered extended Su-Schrieffer-Heeger model
• Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain
• Cooper-pair transistor as a minimal topological quantum circuit
• Engineering Dissipative Quasicrystals
• Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems
• Disorder in dissipation-induced topological states: Evidence for a different type of localization transition
• Topological phase transitions at finite temperature
• Fate of exceptional points under interactions: Reduction of topological classifications
• Observation of a topological edge state stabilized by dissipation
• Non-Hermitian Topology in Hermitian Topological Matter
• Dissipative Boundary State Preparation
• Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder
• Stirring by Staring: Measurement Induced Chirality
• Symmetry-Preserving Quadratic Lindbladian and Dissipation Driven Topological Transitions in Gaussian States
• Chern number and Berry curvature for Gaussian mixed states of fermions
• Correlation effects on non-Hermitian point-gap topology in zero dimension: reduction of topological classification
• Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system
• Fractional Josephson effect versus fractional charge in superconducting-normal metal hybrid circuits
• Interferometry of non-Abelian band singularities and Euler class topology
• Kramers' degeneracy for open systems in thermal equilibrium
• Field theory of non-Hermitian disordered systems
• Generalized Zeno effect and entanglement dynamics induced by fermion counting
• Edge modes and symmetry-protected topological states in open quantum systems
• Spectral and steady-state properties of fermionic random quadratic Liouvillians
• Dissipative dynamics in open XXZ Richardson-Gaudin models
• Skin Effect in Quadratic Lindbladian Systems: an Adjoint Fermion Approach
• Entanglement Transition due to particle losses in a monitored fermionic chain
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Dissipation Induced Flat Bands
• Subradiant edge states in an atom chain with waveguide-mediated hopping
• Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry
• Topological skyrmion phases of matter
• Role of Bath-Induced Many-Body Interactions in the Dissipative Phases of the Su-Schrieffer-Heeger Model
• Information constraint in open quantum systems
• Exact dynamical correlations of nonlocal operators in quadratic open Fermion systems: a characteristic function approach
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Majorana zero-modes in a dissipative Rashba nanowire
• Lindbladian versus Postselected Non-Hermitian Topology
• Symmetry classes of dissipative topological insulators with edge dark state
• Universal hard-edge statistics of non-Hermitian random matrices
• Probing the Topology of Fermionic Gaussian Mixed States with {U(1)} symmetry by Full Counting Statistics
• Edge-selective extremal damping from topological heritage of dissipative Chern insulators
• Linear and Non-Linear Response of Quadratic Lindbladians
• Topology of Discrete Quantum Feedback Control
• Topological photon pumping in quantum optical systems
• Non-Hermitian topological quantum states in a reservoir-engineered transmon chain
• Time-reversal invariant topological skyrmion phases
• Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk
• Topological classifications of quadratic bosonic excitations in closed and open systems with examples
• Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries
• Fate of symmetry protected coherence in open quantum system
• Symmetry classes of classical stochastic processes
• Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• Finite-temperature topological invariant for higher-order topological insulators
• Topological extension including quantum jump
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Effective Conformal Field Theory generated from Pure and Dephased Chern insulator
• Microtubules as electron-based topological insulators
• Time-dependent driving and topological protection in the fractional Josephson effect
• Dissipation-driven topological phase transitions in open quantum systems independent of system Hamiltonian
• Topological Phases in a PT-Symmetric Dissipative Kitaev Chain
• Robust nonequilibrium edge currents with and without band topology
• Open-system dynamics in local Lindbladians with chaotic spectra
• Symmetry and Topology of Monitored Quantum Dynamics
• Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories?
• Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension
• Effective dynamics of qubit networks via phase-covariant quantum ensembles
• Symmetry-induced even/odd parity in charge and heat pumping
• Characterizing dynamical behaviors in topological open systems with boundary dissipations
• Liouville Fock state lattices and potential simulators
• Robust nonequilibrium surface currents in the 3D Hofstadter model
• Signatures of quantum phases in a dissipative system
• Memory-Critical Dynamical Buildup of Phonon-Dressed Majorana Fermions
• Quantized single-particle Thouless pump induced by topology transfer from a Chern insulator at finite temperature
• Topological signatures in a weakly dissipative Kitaev chain of finite length
• Tenfold Way for Holography : AdS/CFT and Beyond
• Phase Transition of Topological Index driven by Dephasing
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking
• Coupled-wire construction of non-Abelian higher-order topological phases
• Replica Keldysh field theory of quantum-jump processes: General formalism and application to imbalanced and inefficient fermion counting
• Topological states of generalized dissipative Majorana wires
• Simulating monitoring-induced topological phase transitions with small systems
• Antilinear superoperator, quantum geometric invariance, and antilinear symmetry for higher-dimensional quantum systems
• Nonequilibrium dark space phase transition