Universal scaling of finite-temperature quantum adiabaticity in driven many-body systems

TL;DR

This paper derives universal bounds on the rate at which many-body quantum systems can be driven adiabatically at finite temperature, revealing temperature-dependent scaling laws and providing practical criteria for adiabaticity.

Contribution

It introduces a mixed-state quantum speed limit combined with fidelity susceptibility to establish finite-temperature adiabaticity criteria in many-body systems.

Findings

Threshold driving rate factorizes into size-dependent and temperature-dependent parts.

At low temperature, the temperature factor approaches unity; at high temperature, it scales linearly with temperature.

Scaling laws are verified in spin-1/2 chains with explicit formulas for the threshold rate.

Abstract

Establishing quantitative adiabaticity criteria at finite temperature remains substantially less developed than in the pure-state setting, even though realistic quantum systems are never at absolute zero. Here, by combining a mixed-state quantum speed limit with mixed-state fidelity susceptibility within the Liouville-space formulation of quantum mechanics, we derive rigorous bounds on the Hilbert-Schmidt fidelity between mixed states. Focusing on protocols that drive an initial Gibbs state toward a quasi-Gibbs target, these bounds yield an explicit threshold driving rate for the onset of nonadiabaticity. For a broad class of local Hamiltonians in gapped phases, we show that, in the thermodynamic limit, the threshold driving rate factorizes into a system-size contribution that recovers the zero-temperature scaling and a universal temperature-dependent factor. The latter is exponentially close to unity at low temperature, whereas at high temperature it is linear in temperature. We verify the predicted scaling in several spin-1/2 chains by obtaining closed-form expressions for the threshold driving rate. Our results provide a practical and largely model-independent criterion for finite-temperature adiabaticity in driven many-body systems under closed-system unitary evolution.