Universal locality of quantum thermal susceptibility

TL;DR

This paper proves that in locally interacting quantum systems, the precision of local temperature measurements is primarily determined by the local Hamiltonian variance, especially when the subsystem's volume-to-surface ratio exceeds the correlation length.

Contribution

It establishes that the local quantum thermal susceptibility closely approximates the local Hamiltonian variance under broad conditions, extending understanding beyond the canonical ensemble assumption.

Findings

Local quantum thermal susceptibility is close to local Hamiltonian variance.

The approximation holds when the subsystem's volume-to-surface ratio is large compared to the correlation length.

Interactions affect temperature measurement precision only in specific regimes.

Abstract

The ultimate precision of any measurement of the temperature of a quantum system is the inverse of the local quantum thermal susceptibility [De Pasquale et al., Nature Communications 7, 12782 (2016)] of the subsystem with whom the thermometer interacts. If this subsystem can be described with the canonical ensemble, such quantity reduces to the variance of the local Hamiltonian, that is proportional to the heat capacity of the subsystem. However, the canonical ensemble might not apply in the presence of interactions between the subsystem and the rest of the system. In this work we address this problem in the framework of locally interacting quantum systems. We prove that the local quantum thermal susceptibility of any subsystem is close to the variance of its local Hamiltonian, provided the volume to surface ratio of the subsystem is much larger than the correlation length. This result greatly simplifies the determination of the ultimate precision of any local estimate of the temperature, and rigorously determines the regime where interactions can affect this precision.