Temperature and integrability-breaking correspondence via adiabatic transformations

TL;DR

This paper demonstrates that lowering temperature in many-body systems guides them toward integrability, linking temperature to chaos and integrability-breaking through geometric and adiabatic analysis.

Contribution

It establishes a novel correspondence between temperature and integrability-breaking, showing temperature as a control parameter for chaos in classical and quantum systems.

Findings

Slow relaxation of local observables near the integrable point.

Scaling relations of fidelity susceptibility resemble phase transitions.

Dynamical exponents vary between quantum and classical models.

Abstract

We reveal a correspondence between temperature and integrability-breaking in classical and quantum many-body systems through the lens of geometry and adiabatic transformations. Decreasing the temperature, obtained in a standard way through the derivative of entropy with respect to energy, steers the system towards an integrable point despite strong integrability-breaking interactions. Auto-correlation functions of local observables exhibit slow relaxation dynamics, which violates ergodicity on the approach to this integrable point. Subsequently, the average fidelity susceptibility of stationary states satisfies scaling relations near the integrable point, in close analogy with continuous phase transitions. We further find that the dynamical exponent encompassing relaxation can be different in the quantum and classical models, depending on dimension of the systems. Collectively, our results establish temperature as a tunable control parameter for chaos and puts it on equal footing with integrability-breaking perturbations.