Local temperature in quantum thermal states

TL;DR

This paper investigates how local temperature in quantum spin chains deviates from classical expectations, especially near quantum phase transitions, and introduces an effective local temperature concept to better describe subsystems.

Contribution

It demonstrates that local blocks can be approximated as thermal states with an effective temperature, revealing quantum effects on thermodynamical properties.

Findings

Deviations from classical temperature behavior in quantum systems are identified.

Quantum fidelity measures the departure from classical thermal states.

An effective local temperature can accurately describe subsystems.

Abstract

We consider blocks of quantum spins in a chain at thermal equilibrium, focusing on their properties from a thermodynamical perspective. Whereas in classical systems the temperature behaves as an intensive magnitude, a deviation from this behavior is expected in quantum systems. In particular, we see that under some conditions the description of the blocks as thermal states with the same global temperature as the whole chain fails. We analyze this issue by employing the quantum fidelity as a figure of merit, singling out in detail the departure from the classical behavior. The influence in this sense of zero-temperature quantum phase transitions can be clearly observed within this approach. Then we show that the blocks can be considered indeed as thermal states with a high fidelity, provided an effective local temperature is properly identified. Such a result originates from typical properties of reduced sub-systems of energy-constrained Hilbert spaces. Finally, the relation between local and global temperature is analyzed as a function of the size of the blocks and the system parameters.