Rapid thermalization of spin chain commuting Hamiltonians

TL;DR

This paper proves that certain quantum spin chains coupled to a heat bath reach thermal equilibrium rapidly, with the time scaling logarithmically with system size, extending classical results to the quantum domain.

Contribution

It generalizes a classical result to quantum spin chains, showing rapid thermalization and ruling out dissipative phase transitions for a broad class of Hamiltonians.

Findings

Quantum spin chains thermalize in logarithmic time scale.

No dissipative phase transition occurs in the studied models.

Results apply to symmetry-protected topological phases.

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.