Thermometry of Strongly Correlated Fermionic Quantum Systems using Impurity Probes

TL;DR

This paper explores using quantum impurity models as sensitive thermometers for fermionic environments, revealing different regimes of sensitivity and universality depending on the impurity-environment interaction type.

Contribution

It introduces a detailed analysis of impurity-based thermometry, highlighting the impact of Ising and Kondo couplings on sensitivity and uncovering universal low-temperature behavior.

Findings

Ising impurities achieve sensitivity comparable to ideal two-level systems.

Kondo impurities exhibit enhanced thermometric response due to many-body entanglement.

Universal low-temperature thermometric regime governed by environment spectral features.

Abstract

We study quantum impurity models as a platform for quantum thermometry. A single quantum spin-1/2 impurity is coupled to an explicit, structured, fermionic thermal environment which we refer to as the environment or bath. We critically assess the thermometric capabilities of the impurity as a probe, when its coupling to the environment is of Ising or Kondo exchange type. In the Ising case, we find sensitivity equivalent to that of an idealized two-level system, with peak thermometric performance obtained at a temperature that scales linearly in the applied control field, independent of the coupling strength and environment spectral features. By contrast, a richer thermometric response can be realized for Kondo impurities, since strong probe-environment entanglement can then develop. At low temperatures, we uncover a regime with a universal thermometric response that is independent of microscopic details, controlled only by the low-energy spectral features of the environment. The many-body entanglement that develops in this regime means that low-temperature thermometry with a weakly applied control field is inherently less sensitive, while optimal sensitivity is recovered by suppressing the entanglement with stronger fields.