Boosting thermalization of classical and quantum many-body systems

TL;DR

This paper introduces a scalable framework for designing Lindbladians that efficiently thermalize many-body systems by optimizing their spectral gap, applicable to both classical and quantum models.

Contribution

The authors develop a systematic, symmetry-respecting variational method to construct Lindbladians that enhance thermalization in many-body systems, scalable with tensor-network techniques.

Findings

Significant enhancement of the spectral gap in classical and quantum spin models.

Framework reveals a relation between finite and infinite temperature relaxation.

Provides bounds on relaxation rates for larger system sizes.

Abstract

Understanding and optimizing the relaxation dynamics of many-body systems is essential both for foundational studies in quantum thermodynamics and for applications such as quantum simulation and quantum computing. Efficient preparation of thermal states of a many-body Hamiltonian is governed by the spectral properties of the associated Lindbladian, in particular its spectral gap, which determines the slowest relaxation rate. In this work, we develop a systematic framework for constructing Lindbladians that prepare thermal states. Our approach reveals a simple relation between the relaxation dynamics at finite and infinite temperatures. The framework is scalable to larger system sizes when implemented using tensor-network methods. We find that efficient thermalization requires that the relaxation dynamics respect the symmetries of the thermal state, which reduces the number of free parameters. By applying gradient-based optimization to the Lindbladians, we enhance the spectral gap and thereby boost thermalization. When applied to both classical and quantum spin models, our method demonstrates a substantial enhancement of the spectral gap. For larger system sizes, our approach provides a variational upper bound and enables a certified lower bound on the minimum relaxation rate.