PT-symmetric quantum Liouvillian dynamics

Abstract

We discuss a combination of unitary and anti-unitary symmetry of quantum Liouvillian dynamics, in the context of open quantum systems, which implies a D2 symmetry of the complex Liovillean spectrum. For sufficiently weak system-bath coupling it implies a uniform decay rate for all coherences, i.e. off-diagonal elements of the system's density matrix taken in the eigenbasis of the Hamiltonian. As an example we discuss symmetrically boundary driven open XXZ spin 1/2 chains.

Note [18] added with respect to a published version, explaining the symmetry of the matrix V [eq. (14)]

References in corpus (17)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Exact nonequilibrium steady state of a strongly driven open XXZ chain
• PT -symmetric harmonic oscillators
• Quantum noise and self-sustained radiation of PT-symmetric systems
• PT-Symmetric Wave Chaos
• Experimental observation of the dual behavior of $\mathcal{P}\mathcal{T}$-symmetric scattering
• Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
• Bypassing the bandwidth theorem with PT symmetry
• Negative differential conductivity in far-from-equilibrium quantum spin chains
• Universal routes to spontaneous PT-symmetry breaking in non-hermitian quantum systems

Cited by in corpus (56)

• Non-Hermitian Physics
• Symmetries and conserved quantities in Lindblad master equations
• Non-Hermitian Many-Body Localization
• Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Matrix product solutions of boundary driven quantum chains
• Breaking of PT-symmetry in bounded and unbounded scattering systems
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Nonlinear sigma models for monitored dynamics of free fermions
• 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
• Symmetry Classification of Many-Body Lindbladians: Tenfold Way and Beyond
• Emergence of PT-symmetry breaking in open quantum systems
• Mean-field validity in a dissipative critical system: Liouvillian gap, $\mathbb{PT}$-symmetric antigap, and permutational symmetry in the $XYZ$ model
• Driven-dissipative phase transition in a Kerr oscillator: From semiclassical $\mathcal{P}\mathcal{T}$ symmetry to quantum fluctuations
• The non-reciprocal Dicke model
• Exactly solvable counting statistics in weakly coupled open interacting spin systems
• Large-deviation statistics of a diffusive quantum spin chain and the additivity principle
• Manipulating energy and spin currents in nonequilibrium systems of interacting qubits
• Generating high-order quantum exceptional points in synthetic dimensions
• Symmetry-protected coherent relaxation of open quantum systems
• Nonreciprocal Synchronization of Active Quantum Spins
• $\mathcal{P}\mathcal{T}$ phase transition in open quantum systems with Lindblad dynamics
• Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Topological phases protected by shifted sublattice symmetry in dissipative quantum systems
• Renyi Entropy Dynamics and Lindblad Spectrum for Open Quantum System
• Parity-time symmetry-breaking mechanism of dynamic Mott transitions in dissipative systems
• Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain
• Exterior integrability: Yang-Baxter form of nonequilibrium steady state density operator
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• Generic examples of PT-symmetric qubit (spin 1/2) Liouvillians
• Quantum Ising chain with boundary dephasing
• Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
• Dissipative time crystals originating from parity-time symmetry
• Quasiparticles of Decoherence Processes in Open Quantum Many-Body Systems: Incoherentons
• Geometric energy transport and refrigeration with driven quantum dots
• Dissipative dynamics in open XXZ Richardson-Gaudin models
• Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry
• Kondo effect in a non-Hermitian, $\mathcal{P}\mathcal{T}$-symmetric Anderson model with Rashba spin-orbit coupling
• Full decoherence induced by local fields in open spin chains with strong boundary couplings
• Mixed states driven by Non-Hermitian Hamiltonians of a nuclear spin ensemble
• Operator size growth in Lindbladian SYK
• Unbalanced gain and loss in a quantum photonic system
• Universal hard-edge statistics of non-Hermitian random matrices
• Trigonometric SU(N) Richardson-Gaudin models and dissipative multi-level atomic systems
• Generation of entanglement and non-stationary states via competing coherent and incoherent bosonic hopping
• Spontaneous symmetry breaking in non-steady modes of open quantum many-body systems
• Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor
• Symmetry classes of classical stochastic processes
• Fermionic duality: General symmetry of open systems with strong dissipation and memory
• Topological Phases in a PT-Symmetric Dissipative Kitaev Chain
• Continuous time crystals as a PT symmetric state and the emergence of critical exceptional points
• Parity-Time Symmetric Spin-1/2 Richardson-Gaudin Models
• Hierarchy of degenerate stationary states in a boundary-driven dipole-conserving spin chain
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking
• Time Glasses: Symmetry Broken Chaotic Phase with a Finite Gap