On Which Length Scales Can Temperature Exist in Quantum Systems?

TL;DR

This paper investigates the conditions under which temperature can be meaningfully defined at different length scales in quantum systems, revealing a dependence on temperature and quantum correlations.

Contribution

It introduces a criterion for when quantum systems' states can be approximated as products of local thermal states, highlighting the quantum-specific dependence on temperature.

Findings

Minimum group size for local temperature depends on temperature in quantum systems.

Quantum correlations influence the scale at which temperature can be defined.

Application to Heisenberg spin chains demonstrates the theory's practical relevance.

Abstract

We consider a regular chain of elementary quantum systems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature $T$. We analyze under what condition the state factors into a product of canonical density matrices with respect to groups of $n$ subsystems each, and when these groups have the same temperature $T$. While in classical mechanics the validity of this procedure only depends on the size of the groups $n$, in quantum mechanics the minimum group size $n_{\text{min}}$ also depends on the temperature $T $! As examples, we apply our analysis to different types of Heisenberg spin chains.