Many-body Liouvillian dynamics with a non-Hermitian tensor-network kernel polynomial algorithm
arXiv:2407.06282 · doi:10.1103/PhysRevResearch.6.043182
Abstract
Understanding the dynamics of open quantum many-body systems is a major problem in quantum matter. Specifically, efficiently solving the spectrum of the Liouvillian superoperator governing such dynamics remains a critical open challenge. Here, we put forward a method for solving the many-body Liouvillian spectrum and dynamics based on the non-Hermitian kernel polynomial method and tensor-network techniques. We demonstrate the faithfulness of our method by computing the dynamics of the dephasing quantum compass model with a gradient magnetic field and comparing it with exact results. In particular, we show that our method allows us to characterize the quantum Zeno crossover and the reduction of relaxation rate due to Stark localization in this model. We further demonstrate the ability of our method to go beyond exact results by exploring nearest-neighbor interaction effects on the Liouvillian dynamics, elucidating the interplay between Stark localization and many-body interactions. Our method provides an efficient solution to many-body Liouvillian spectrum and dynamics, establishing a methodology to explore large open quantum many-body systems.
11 pages, 7 figures. Source codes are available at https://github.com/GUANGZECHEN/NHKPM.jl
References in corpus (51)
- Nonequilibrium dynamics of closed interacting quantum systems
- The Kernel Polynomial Method
- The ITensor Software Library for Tensor Network Calculations
- Time-dependent variational principle for quantum lattices
- Unifying time evolution and optimization with matrix product states
- Preparation of Entangled States by Quantum Markov Processes
- Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
- Non-Hermitian skin effect and chiral damping in open quantum systems
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Spectral theory of Liouvillians for dissipative phase transitions
- Exact nonequilibrium steady state of a strongly driven open XXZ chain
- Stark many-body localization
- Algebraic versus exponential decoherence in dissipative many-particle systems
- Simulation methods for open quantum many-body systems
- From Bloch Oscillations to Many Body Localization in Clean Interacting Systems
- Relaxation times of dissipative many-body quantum systems
- Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
- Non-equilibrium dynamics of bosonic atoms in optical lattices: Decoherence of many-body states due to spontaneous emission
- Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos
- Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise
- Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems
- Dissipative spin chain as a non-Hermitian Kitaev ladder
- Anomalous momentum diffusion in a dissipative many-body system
- Decoherence Induced Exceptional Points in a Dissipative Superconducting Qubit
- Exact Nonequilibrium Steady State of an Open Hubbard Chain
- Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
- Stable Quantum-Correlated Many Body States through Engineered Dissipation
- Majorana Modes in Driven-Dissipative Atomic Superfluids With Zero Chern Number
- Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
- Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain
- Dissipation-induced d-Wave Pairing of Fermionic Atoms in an Optical Lattice
- Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems
- Hierarchy of relaxation timescales in local random Liouvillians
- Facilitated spin models of dissipative quantum glasses
- Probing Complex-energy Topology via Non-Hermitian Absorption Spectroscopy in a Trapped Ion Simulator
- Entanglement dynamics of a many-body localized system coupled to a bath
- Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity
- Bath-induced decay of Stark many-body localization
- Topological spin excitations in non-Hermitian spin chains with a generalized kernel polynomial algorithm
- Non-Hermitian Absorption Spectroscopy
- Lieb-Schultz-Mattis Theorem in Open Quantum Systems
- Topological spin excitations in Harper-Heisenberg spin chains
- Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport
- Dynamical universality classes towards an infinite temperature state
- Embedding Quantum Many-Body Scars into Decoherence-Free Subspaces
- Unification of quantum Zeno-anti Zeno effects and parity-time symmetry breaking transitions
- Random matrix theory for quantum and classical metastability in local Liouvillians
- Exact dynamics of quantum dissipative models: Wannier-Stark localization in the fragmented operator space
- Non-Unitary Quantum Many-Body Dynamics using the Faber Polynomial Method
- Solvable BCS-Hubbard Liouvillians in arbitrary dimensions
- Relaxation of imbalance in a disordered XX model with on-site dephasing
Cited by in corpus (5)
- Simulating open quantum systems with giant atoms
- Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites
- Polynomially restricted operator growth in dynamically integrable models
- Tensor network method for real-space topology in quasicrystal Chern mosaics
- Diffusion in quantum state preparation: From passive cooling to system-bath engineering