Rapid thermalization of spin chain commuting Hamiltonians

Abstract

We prove that spin chains weakly coupled to a large heat bath thermalize rapidly at any temperature for finite-range, translation-invariant commuting Hamiltonians, reaching equilibrium in a time which scales logarithmically with the system size. Our main result is a generalization to the quantum setting of a seminal result of Holley and Stroock for classical spin chains and represents an exponential improvement over bounds based on the non-closure of the spectral gap. From a physical point of view, our result rigorously establishes the absence of dissipative phase transition for Davies evolutions over translation-invariant spin chains. The result also applies in the case of Symmetry Protected Topological phases where the evolution is respecting the symmetry of the phase. This has wide-ranging applications to the study of many-body in and out-of-equilibrium quantum systems.

5 pages + 3 pages, 3 figures

References in corpus (62)

• Quantum Machine Learning
• Persistent entanglement in arrays of interacting particles
• Entanglement spectrum of a topological phase in one dimension
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Quantum Orders and Symmetric Spin Liquids
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Topological phases of fermions in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Classifying quantum phases using Matrix Product States and PEPS
• Topology by Dissipation in Atomic Quantum Wires
• Symmetries and conserved quantities in Lindblad master equations
• Spectral theory of Liouvillians for dissipative phase transitions
• Topological quantum order: stability under local perturbations
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Dissipative Phase Transition in Central Spin Systems
• Quantum Metropolis Sampling
• Majorana qubit decoherence by quasiparticle poisoning
• Noncommutative vector valued $L_p$-spaces and completely $p$-summing maps
• Topology by dissipation
• Quantum Simulations of Classical Annealing Processes
• Tomography and Generative Data Modeling via Quantum Boltzmann Training
• On thermalization in Kitaev's 2D model
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Quantum logarithmic Sobolev inequalities and rapid mixing
• Quantum phase transition between cluster and antiferromagnetic states
• Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field
• Symmetry Protected Topological Order in Open Quantum Systems
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• An order parameter for symmetry-protected phases in one dimension
• Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
• Observation of topological Uhlmann phases with superconducting qubits
• Symmetry classes of open fermionic quantum matter
• Adequacy of Si:P Chains as Fermi-Hubbard Simulators
• Symmetry protected topological order at nonzero temperature
• Thermal Instability of Protected End States in a 1-D Topological Insulator
• Stability of local quantum dissipative systems
• Classification of phases for mixed states via fast dissipative evolution
• Hypercontractivity of quasi-free quantum semigroups
• Survey on Nonlocal Games and Operator Space Theory
• Fragility of Time-Reversal Symmetry Protected Topological Phases
• Symmetry-protected Topological Phases at Finite Temperature
• Complete entropic inequalities for quantum Markov chains
• Exponential decay of mutual information for Gibbs states of local Hamiltonians
• Irreducible forms of Matrix Product States: Theory and Applications
• Dissipation-driven quantum phase transitions in collective spin systems
• Dissipation-driven phase transition in 2D Josephson arrays
• Quantum conditional relative entropy and quasi-factorization of the relative entropy
• On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems
• The modified logarithmic Sobolev inequality for quantum spin systems: classical and commuting nearest neighbour interactions
• Interacting Symmetry-Protected Topological Phases Out of Equilibrium
• Rapid mixing and stability of quantum dissipative systems
• Approximate tensorization of the relative entropy for noncommuting conditional expectations
• Inaccessible entanglement in symmetry protected topological phases
• Self correction requires Energy Barrier for Abelian quantum doubles
• Super-operator structures and no-go theorems for dissipative quantum phase transitions
• Thermalization in Kitaev's quantum double models via Tensor Network techniques
• Quantum Hamiltonian complexity and the detectability lemma
• Quasi-factorization and Multiplicative Comparison of Subalgebra-Relative Entropy
• Classification of gapped ground state phases in quantum spin systems
• Hypercontractivity and logarithmic Sobolev Inequality for non-primitive quantum Markov semigroups and estimation of decoherence rates

Cited by in corpus (29)

• Single-ancilla ground state preparation via Lindbladians
• Exponential decay of mutual information for Gibbs states of local Hamiltonians
• Quantum many-body systems in thermal equilibrium
• Efficient quantum Gibbs samplers with Kubo--Martin--Schwinger detailed balance condition
• Entropy decay for Davies semigroups of a one dimensional quantum lattice
• Continuity of quantum entropic quantities via almost convexity
• Rapid quantum ground state preparation via dissipative dynamics
• Optimal quantum algorithm for Gibbs state preparation
• Dissipative Preparation of Many-Body Quantum States: Towards Practical Quantum Advantage
• Rapid thermalization of dissipative many-body dynamics of commuting Hamiltonians
• Accuracy guarantees and quantum advantage in analogue open quantum simulation with and without noise
• Quantum computational advantage with constant-temperature Gibbs sampling
• General Continuity Bounds for Quantum Relative Entropies
• Mixing Time of Open Quantum Systems via Hypocoercivity
• The Wasserstein distance of order 1 for quantum spin systems on infinite lattices
• Clustering theorem in 1D long-range interacting systems at arbitrary temperatures
• Entanglement Properties of SU(2) Gauge Theory
• Area law for steady states of detailed-balance local Lindbladians
• Quantum Enhancement of Thermalization
• Bounds on Autonomous Quantum Error Correction
• Emergence of the Gibbs ensemble as a steady state in Lindbladian dynamics
• A little bit of self-correction
• Strong decay of correlations for Gibbs states in any dimension
• Simple and efficient end-to-end quantum thermal and ground state preparation
• Gibbs state sampling via cluster expansions
• Variational Quantum Algorithms for Gibbs State Preparation
• Dissipative ground state preparation in ab initio electronic structure theory
• Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains
• Operator-Level Quantum Acceleration of Non-Logconcave Sampling