Spectral theory of Liouvillians for dissipative phase transitions

Abstract

A state of an open quantum system is described by a density matrix, whose dynamics is governed by a Liouvillian superoperator. Within a general framework, we explore fundamental properties of both first-order dissipative phase transitions and second-order dissipative phase transitions associated with a symmetry breaking. In the critical region, we determine the general form of the steady-state density matrix and of the Liouvillian eigenmatrix whose eigenvalue defines the Liouvillian spectral gap. We illustrate our exact results by studying some paradigmatic quantum optical models exhibiting critical behavior.

14 pages, 7 figures

References in corpus (27)

• Probing many-body dynamics on a 51-atom quantum simulator
• Quantum fluids of light
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Quantum trajectories and open many-body quantum systems
• Dissipative Phase Transition in Central Spin Systems
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Adiabatic approximation in open quantum systems
• Variational principle for steady states of dissipative quantum many-body systems
• Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
• Critical dynamical properties of a first-order dissipative phase transition
• Signatures of a dissipative phase transition in photon correlation measurements
• Observation of the photon-blockade breakdown phase transition
• Analysis of quantum semigroups with GKS--Lindblad generators II. General
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Critical slowing down in driven-dissipative Bose-Hubbard lattices
• Light-mediated cascaded locking of multiple nano-optomechanical oscillators
• Limit cycle phase in driven-dissipative spin systems
• Quantum entanglement in the spatial symmetry breaking phase transition of a driven-dissipative Bose-Hubbard dimer
• Hybrid systems for the generation of non-classical mechanical states via quadratic interactions
• Parametric symmetry breaking in a nonlinear resonator
• Linked cluster expansions for open quantum systems on a lattice
• Dynamical properties of dissipative XYZ Heisenberg lattices
• A driven-dissipative quantum Monte Carlo method for open quantum systems
• Dissipative quantum phase transition of light in a generalized Jaynes-Cummings-Rabi model
• Spatial correlations in driven-dissipative photonic lattices

Cited by in corpus (277)

• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Critical Quantum metrology with a finite-component quantum phase transition
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Variational neural network ansatz for steady states in open quantum systems
• Geometry of quantum phase transitions
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
• Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains
• Quantum critical regime in a quadratically-driven nonlinear photonic lattice
• Symmetry breaking and error correction in open quantum systems
• Critical parametric quantum sensing
• Squeezed light induced symmetry breaking superradiant phase transition
• Lindblad dissipative dynamics in presence of phase coexistence
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Multistability of Driven-Dissipative Quantum Spins
• A quantum transducer using a parametric driven-dissipative phase transition
• Generating Large Cats with Nine Lives: Long-Lived Macroscopically Distinct Superposition States in Atomic Ensembles
• Coherent and dissipative dynamics at quantum phase transitions
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• A Tutorial on Quantum Master Equations: Tips and tricks for quantum optics, quantum computing and beyond
• A dissipative time crystal in an asymmetric non-linear photonic dimer
• Driven-dissipative quantum Kerr resonators: new exact solutions, photon blockade and quantum bistability
• Spectral gaps and mid-gap states in random quantum master equations
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Liouvillian Skin Effect in an Exactly Solvable Model
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Quantum squeezing and sensing with pseudo anti-parity-time symmetry
• Observation of quantum strong Mpemba effect
• Robustness of exceptional-point-based sensors against parametric noise: The role of Hamiltonian and Liouvillian degeneracies
• Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$ symmetries
• Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory
• Signatures of Liouvillian exceptional points in a quantum thermal machine
• Symmetries and Conservation Laws in Quantum Trajectories: Dissipative Freezing
• Random Lindblad Dynamics
• Driven Bose-Hubbard dimer under nonlocal dissipation: A bistable time crystal
• Quantum metrology with boundary time crystals
• Phase diagram of the dissipative quantum Ising model on a square lattice
• Dissipative quantum Ising chain as a non-Hermitian Ashkin-Teller model
• Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law
• Critical Quantum Metrology in the Non-Linear Quantum Rabi Model
• Critical Quantum Metrology with Fully-Connected Models: From Heisenberg to Kibble-Zurek Scaling
• Mean-field validity in a dissipative critical system: Liouvillian gap, $\mathbb{PT}$-symmetric antigap, and permutational symmetry in the $XYZ$ model
• Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
• Distinctive class of dissipation-induced phase transitions and their universal characteristics
• Driven-dissipative phase transition in a Kerr oscillator: From semiclassical $\mathcal{P}\mathcal{T}$ symmetry to quantum fluctuations
• Exact solutions of interacting dissipative systems via weak symmetries
• Measurement Induced Continuous Time Crystals
• A quantum battery with quadratic driving
• Dissipative Topological Phase Transition with Strong System-Environment Coupling
• Accelerating relaxation through Liouvillian exceptional point
• Theory of classical metastability in open quantum systems
• Rapid thermalization of spin chain commuting Hamiltonians
• Open Quantum System Dynamics from Infinite Tensor Network Contraction
• Non-equilibrium magnetic phases in spin lattices with gain and loss
• Critical slowing down in the bistable regime of circuit quantum electrodynamics
• Quantum behavior of a superconducting Duffing oscillator at the dissipative phase transition
• Spectral functions and negative density of states of a driven-dissipative nonlinear quantum resonator
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Dynamical quantum phase transitions in SYK Lindbladians
• Dissipation as a resource for Quantum Reservoir Computing
• Quantum description of surface-enhanced resonant Raman scattering within a hybrid-optomechanical model
• Gaussian trajectory approach to dissipative phase transitions: the case of quadratically driven photonic lattices
• Mesoscopic limit cycles in coupled nanolasers
• Observation of first- and second-order dissipative phase transitions in a two-photon driven Kerr resonator
• Dissipation-induced bistability in the two-photon Dicke model
• 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
• Experimental observation of a dissipative phase transition in a multi-mode many-body quantum system
• Solving the Liouvillian Gap with Artificial Neural Networks
• Breaking strong symmetries in dissipative quantum systems: Bosonic atoms coupled to a cavity
• Topological phases protected by shifted sublattice symmetry in dissipative quantum systems
• Spontaneous symmetry breaking in a coherently driven nanophotonic Bose-Hubbard dimer
• Dissipative phase transitions in the fully-connected Ising model with $p$-spin interaction
• A dissipative time crystal with or without ${\mathbb{Z}}_2$ symmetry breaking
• Criticality-Enhanced Quantum Sensing with a Parametric Superconducting Resonator
• From integrability to chaos in quantum Liouvillians
• Liouvillian spectral collapse in the Scully-Lamb laser model
• Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems
• The driven-dissipative Bose-Hubbard dimer: phase diagram and chaos
• Dissipative phase transitions in $n$-photon driven quantum nonlinear resonators
• Many-Body Open Quantum Systems
• Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect
• Linear-and-quadratic reservoir engineering of non-Gaussian states
• Quantum metrology with critical driven-dissipative collective spin system
• Adiabatic Elimination and Sub-space Evolution of Open Quantum Systems
• Engineered dissipation to mitigate barren plateaus
• Few-mode geometric description of a driven-dissipative phase transition in an open quantum system
• Critical Theory for the Breakdown of Photon Blockade
• Liouvillian Dynamics of the Open Schwinger Model: String Breaking and Kinetic Dissipation in a Thermal Medium
• The bosonic skin effect: boundary condensation in asymmetric transport
• Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories
• Generation of a maximally entangled state using collective optical pumping
• Quantum critical systems with dissipative boundaries
• Experimental Liouvillian exceptional points in a quantum system without Hamiltonian singularities
• Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops
• Sufficient condition for gapless spin-boson Lindbladians, and its connection to dissipative time-crystals
• Optimal stochastic unraveling of disordered open quantum systems: application to driven-dissipative photonic lattices
• Diverging current fluctuations in critical Kerr resonators
• Quantum Ising chain with boundary dephasing
• Accelerating Relaxation Dynamics in Open Quantum System with Liouvillian Skin Effect
• Quantum non-stationary phenomena of spin systems in collision models
• On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices
• Nonperturbative cavity quantum electrodynamics: is the Jaynes-Cummings model still relevant?
• Enhanced Two-Parameter Phase-Space-Displacement Estimation Close to Dissipative Phase Transition
• Atom-only theories for U(1) symmetric cavity-QED models
• Multi-Photon Resonances in Josephson Junction-Cavity Circuits
• Dissipative phase transition with driving-controlled spatial dimension and diffusive boundary conditions
• Quantum features of entropy production in driven-dissipative transitions
• Simulating frustrated antiferromagnets with quadratically driven QED cavities
• Universal subdiffusive behavior at band edges from transfer matrix exceptional points
• Low- and high-$\beta$ lasers in Class-A limit: photon statistics, linewidth, and the laser-phase transition analogy
• Multicritical dissipative phase transitions in the anisotropic open quantum Rabi model
• Quantum associative memory with a single driven-dissipative nonlinear oscillator
• Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Dissipative time crystals originating from parity-time symmetry
• Sub-diffusive phases in open clean long-range systems
• Synchronization of persistent oscillations in spin systems with non-local dissipations
• Classical critical dynamics in quadratically driven Kerr resonators
• Correlation-induced steady states and limit cycles in driven dissipative quantum systems
• Nonequilibrium transition between dissipative time crystals
• Critical phenomena and nonlinear dynamics in a spin ensemble strongly coupled to a cavity. I. Semiclassical approach
• Quasiparticles of Decoherence Processes in Open Quantum Many-Body Systems: Incoherentons
• Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems
• Probing a dissipative phase transition with a trapped ion through reservoir engineering
• Dissipative phase transitions in optomechanical systems
• Nonequilibrium thermodynamics and power generation in open quantum optomechanical systems
• Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems
• Parametrically driving a quantum oscillator into exceptionality
• Non-Gaussian superradiant transition via three-body ultrastrong coupling
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• Quantum density matrix theory for a laser without adiabatic elimination of the population inversion: transition to lasing in the class-B limit
• Controlling Matter Phases beyond Markov
• Quantum dynamics of Dissipative Kerr solitons
• Projection based adiabatic elimination of bipartite open quantum systems
• Variational truncated Wigner approximation for weakly interacting Bose fields: Dynamics of coupled condensates
• A quantum algorithm for the direct estimation of the steady state of open quantum systems
• Monte Carlo matrix-product-state approach to the false vacuum decay in the monitored quantum Ising chain
• Dissipative Quantum Chaos unveiled by Stochastic Quantum Trajectories
• Topological transitions in quantum jump dynamics: Hidden exceptional points
• Feedback-stabilized dynamical steady states in the Bose-Hubbard model
• Rapid thermalization of dissipative many-body dynamics of commuting Hamiltonians
• Relaxation breakdown and resonant tunneling in ultrastrong-coupling cavity QED
• The effect of thermal photons on exceptional points in coupled resonators
• Non-Markovian skin effect
• Unravelling Metastable Markovian Open Quantum Systems
• Signatures of Self-Trapping in the Driven-Dissipative Bose-Hubbard Dimer
• Super-operator structures and no-go theorems for dissipative quantum phase transitions
• Dissipative quantum state preparation and metastability in two-photon micromasers
• Periodically Driven Open Quantum Systems: Spectral Properties and Non-Equilibrium Steady States
• Adaptive variational low-rank dynamics for open quantum systems
• Dynamical quantum phase transition in diamond: applications in quantum metrology
• Qubit Decoherence and Symmetry Restoration through Real-Time Instantons
• Asymmetries of thermal processes in open quantum systems
• Trajectory tracking for non-Markovian quantum systems
• Universal equilibration dynamics of the Sachdev-Ye-Kitaev model
• Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
• Exceptional points and exponential sensitivity for periodically driven Lindblad equations
• Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems
• Nonuniform phases in the geometrically frustrated dissipative XYZ model
• Dawn and fall of non-Gaussianity in the quantum parametric oscillator
• Spectral signatures of symmetry-breaking dynamical phase transitions
• Topologically Ordered Steady States in Open Quantum Systems
• Exact dynamical correlations of nonlocal operators in quadratic open Fermion systems: a characteristic function approach
• Fate of non-Hermitian free fermions with Wannier-Stark ladder
• Interaction-Enhanced Superradiance of a Ryderg-Atom Array
• Quantum memories for squeezed and coherent superpositions in a driven-dissipative nonlinear oscillator
• Quantum Mpemba effect in parity-time symmetric systems
• Spectral theory of non-Markovian dissipative phase transitions
• Dissipative phase transition in systems with two-photon drive and nonlinear dissipation near the critical point
• Non-Floquet engineering in periodically driven non-Hermitian systems
• Chaotic and quantum dynamics in driven-dissipative bosonic chains
• Fluctuation-Induced Bistability of Fermionic Atoms Coupled to a Dissipative Cavity
• Transport and spectral properties of the XX$+$XXZ diode and stability to dephasing
• Measurement-Induced Spectral Transition
• Crossover from the discontinuous to continuous phase transitions in dissipative spin system with collective decay
• Unbalanced gain and loss in a quantum photonic system
• Non-stationary dynamics and dissipative freezing in squeezed superradiance
• Dynamical signatures of discontinuous phase transitions: How phase coexistence determines exponential versus power-law scaling
• Entropy production dynamics in quench protocols of a driven-dissipative critical system
• Steady-state phases of dissipative spin-1/2 XYZ model with frustrated interaction
• Adiabatic quantum trajectories in engineered reservoirs
• Number of steady states of quantum evolutions
• Dynamical Signatures of Liouvillian Flat Band
• Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries
• Symmetries & Correlations in Continous Time Crystals
• Breakdown of Measurement-Induced Phase Transitions Under Information Loss
• Exceptional stationary state in a dephasing many-body open quantum system
• Time- and frequency-domain two-particle correlations of a driven dissipative Bose-Hubbard model
• Trigonometric SU(N) Richardson-Gaudin models and dissipative multi-level atomic systems
• Strong-coupling limit of the driven dissipative light-matter interaction
• Liouvillian exceptional points in continuous variable system
• Steady-state susceptibility in continuous phase transitions of dissipative systems
• A trapped ion in an optical cavity: numerical study of an optomechanical transition in the few-photon regime
• Non-equilibrium steady states and critical slowing down in the dissipative Bose-Hubbard model
• Information geometry of transitions between quantum nonequilibrium steady states
• Optical pumping through the Liouvillian skin effect
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Many-body Liouvillian dynamics with a non-Hermitian tensor-network kernel polynomial algorithm
• Dynamical phase transition in a strongly hybridized phonon-triplon chain
• Symmetries of Liouvillians of squeeze-driven parametric oscillators
• Liouville Space Neural Network Representation of Density Matrices
• Correspondence between dissipative phase transitions of light and time crystals
• Identifying an environment-induced localization transition from entropy and conductance
• Exploiting nonequilibrium phase transitions and strong symmetries for continuous measurement of collective observables
• Oscillating-mode gap: an indicator of phase transition in open quantum many-body systems
• Genuine Quantum effects in Dicke-type Models at large atom numbers
• Absence of operator growth for average equal-time observables in charge-conserved sectors of the Sachdev-Ye-Kitaev model
• Spectroscopic estimation of the photon number for superconducting Kerr parametric oscillators
• Single-photon induced instabilities in a cavity electromechanical device
• Spontaneous symmetry breaking in non-steady modes of open quantum many-body systems
• Stabilization of cat-state manifolds using nonlinear reservoir engineering
• Critical Quantum Sensing: a tutorial on parameter estimation near quantum phase transitions
• Defect production due to time-dependent coupling to environment in the Lindblad equation
• Quantum Mpemba Effect Induced by Non-Markovian Exceptional Points
• Quantum Dissipative Search via Lindbladians
• Dephasing-induced growth of discrete crystalline order in spin networks
• Emergent equilibrium and quantum criticality in a two-photon dissipative oscillator
• Conformal symmetry in quasi-free Markovian open quantum systems
• Dynamic Hysteresis Across a Dissipative Multi-Mode Phase Transition
• Dissipative quantum phase transitions monitored by current fluctuations
• Dissipative phase transition: from qubits to qudits
• Exact steady state of quantum van der Pol oscillator: critical phenomena and enhanced metrology
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Quantum synchronization in an all-optical stroboscopic quantum simulator
• Quantum Features of the Thermal Two-Qubit Quantum Rabi Model in Ultra- and Deep-Strong Regimes
• Driven-Dissipative Bose-Einstein Condensation and the Upper Critical Dimension
• Kinetically constrained models constructed from dissipative quantum dynamics
• Single-shot determination of quantum phases via continuous measurements
• Circuit QED Spectra in the Ultrastrong Coupling Regime: How They Differ from Cavity QED
• Quantum hyperspins: Highly nonclassical collective behavior in quantum optical parametric oscillators
• Local Non-Hermitian Hamiltonian Formalism for Dissipative Fermionic Systems and Loss-Induced Population Increase in Fermi Superfluids
• Viewing protected superconducting qubits through the lens of the cat qubit
• Symmetry-induced fragmentation and dissipative time crystal
• Transient dynamics of the quantum Stuart-Landau oscillator
• Quantization of nonlinear non-Hamiltonian systems
• Asymptotic Exceptional Steady States in Dissipative Dynamics
• Reduced Basis Method for Driven-Dissipative Quantum Systems
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss
• A Real-time Instanton Approach to Quantum Activation
• Dynamical symmetry in quantum dissipative models
• Strong symmetries in collision models and physical dilations of covariant quantum maps
• Quantum correlated steady states under competing collective and individual decay
• Learning the dynamics of Markovian open quantum systems from experimental data
• Closed dynamical recursion equations for correlation functions and the application on the construction of Liouvillian spectrum in Lindbladian systems
• Integrals of motion as slow modes in dissipative many-body operator dynamics
• Thermodynamic Geometric Constraint on the Spectrum of Markov Rate Matrices
• Universal quantum melting of quasiperiodic attractors in driven-dissipative cavities
• Separation of relaxation timescales via strong system-bath coupling: Dissipative three-level system as a case study
• Persistent subradiant correlations in a random driven Dicke model
• Quantum Dynamical Signatures of Topological Flow Transitions in Limit Cycle Phases
• Masked states of an atom coupled to a standing-wave cavity mode
• Exceptional Spectral Phase in a Dissipative Collective Spin Model
• Continuous time crystals as a PT symmetric state and the emergence of critical exceptional points
• Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems
• Metastability in the Dissipative Quantum Rabi Model
• Experimental observation of multimode quantum phase transitions in a superconducting Bose-Hubbard simulator
• Chaos and quantum regimes in $n$-photon driven, dissipative bosonic chains
• Enhanced Parameter Estimation with Periodically Driven Quantum Probe
• Dissipative quantum North-East-Center model: steady-state phase diagram, universality and nonergodic dynamics
• Time correlations from steady-state expectation values
• Time Glasses: Symmetry Broken Chaotic Phase with a Finite Gap
• Macroscopic theory of multipartite correlations in permutation-invariant open quantum systems
• Metastable quantum entrainment
• Pauli crystal superradiance
• Variational Quantum Algorithm for Solving the Liouvillian Gap
• Parameter estimation with one- and two-time measurements on the emission field of the boundary time crystal
• Error bounds on the universal Lindblad equation in the thermodynamic limit
• Metastable discrete time-crystal resonances in a dissipative central spin system
• Lindblad master equations for quantum systems coupled to dissipative bosonic modes
• Josephson oscillation in the dissipative Bose-Hubbard dimer
• Passive leakage removal unit based on a disordered transmon array
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking
• Dynamics of a dispersively coupled transmon qubit in the presence of a noise source embedded in the control line
• Emergence of Rich Dissipative Phases in the Anisotropic Quantum Rabi Model Driven by the $A^2$ Term
• Higher-order Liouvillian exceptional points in the dissipative dynamics of quadratic fermions