Exact solution of the boundary-dissipated transverse field Ising model: Structure of Liouvillian spectrum and dynamical duality

Abstract

We study the boundary-dissipated transverse field Ising model described by a Lindblad Master equation and exactly solve its Liouvillian spectrum in the whole parameter space. By mapping the Liouvillian into a Su-Schrieffer-Heeger model with imaginary boundary potentials under a parity constraint, we solve the rapidity spectrum analytically and thus construct the Liouvillian spectrum strictly with a parity constraint condition. Our results demonstrate that the Liouvillian spectrum displays four different structures, which are characterized by different numbers of segments. By analyzing the properties of rapidity spectrum, we can determine the phase boundaries between different spectrum structures analytically and prove the Liouvillian gap fulfilling a duality relation in the weak and strong dissipation region. Furthermore, we unveil the existence of a dynamical duality, i.e., the long-time relaxation dynamics exhibits almost the same dynamical behavior in the weak and strong dissipation region as long as the duality relation holds true.

arXiv comment15 pages, 10 figures

References in corpus (30)

• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Exact nonequilibrium steady state of a strongly driven open XXZ chain
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Algebraic versus exponential decoherence in dissipative many-particle systems
• Matrix product simulations of non-equilibrium steady states of quantum spin chains
• Simulation methods for open quantum many-body systems
• Quantum simulation of open-system dynamical maps with trapped ions
• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
• Relaxation times of dissipative many-body quantum systems
• Quantum phase transition in a far from equilibrium steady state of XY spin chain
• Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise
• Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
• Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model
• A simple tensor network algorithm for two-dimensional steady states
• Relation between $\mathcal{P}\mathcal{T}$-symmetry breaking and topologically nontrivial phases in the SSH and Kitaev models
• Dissipative spin chain as a non-Hermitian Kitaev ladder
• Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems
• Solutions for dissipative quadratic open systems: part I - bosons
• Solutions for dissipative quadratic open systems: part II - fermions
• Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions
• Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries
• Conventional quantum phase transition driven by complex parameter in non-Hermitian PT-symmetric Ising model
• Renyi Entropy Dynamics and Lindblad Spectrum for Open Quantum System
• Analytical solutions for a boundary driven XY chain
• Full spectrum of the Liouvillian of open dissipative quantum systems in the Zeno limit
• Quantum Ising chain with boundary dephasing
• Geometric phase and phase diagram for non-Hermitian quantum XY model
• Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
• Anomalous relaxation and multiply time scales in the quantum $XY$ model with boundary dissipation

Cited by in corpus (11)

• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations
• Rapid quantum ground state preparation via dissipative dynamics
• Manipulating the Relaxation Time of Boundary-Dissipative Systems through Bond Dissipation
• Zeno physics of the Ising chain with symmetry-breaking boundary dephasing
• Exact density profile in a tight-binding chain with dephasing noise
• Emergence of the Gibbs ensemble as a steady state in Lindbladian dynamics
• A General Strategy for Realizing Mpemba Effects in Open Quantum Systems
• Dissipation meets conformal interface in open quantum systems: How the relaxation rate is suppressed
• Closed dynamical recursion equations for correlation functions and the application on the construction of Liouvillian spectrum in Lindbladian systems
• Characterizing dynamical behaviors in topological open systems with boundary dissipations
• Separation of relaxation timescales via strong system-bath coupling: Dissipative three-level system as a case study