Theoretical formulations on thermodynamics of quantum impurity systems

TL;DR

This paper develops a theoretical framework for understanding the thermodynamics of quantum impurity systems, linking spectral functions to measurable quantities and exploring differences between bosonic and fermionic cases.

Contribution

It introduces a novel theoretical foundation connecting thermodynamic spectral functions with experimentally measurable spectral densities in quantum impurity systems.

Findings

Relation between thermodynamic spectral functions and local spectral densities established

Differences between bosonic and fermionic impurity systems highlighted

Framework applicable to noninteracting impurity models

Abstract

In this work, we put forward the theoretical foundation toward thermodynamics of quantum impurity systems measurable in experiments. The theoretical developments involve the identifications on two types of thermodynamic entanglement free--energy spectral functions for impurity systems that can be either fermionic or bosonic or combined. Consider further the thermodynamic limit in which the hybrid environments satisfy the Gaussian--Wick's theorem. We then relate the thermodynamic spectral functions to the local quantum impurity systems spectral densities that are often experimentally measurable. Another type of inputs is the bare--bath coupling spectral densities, which could be accurately determined with various methods. Similar relation is also established for the nonentanglement component that exists only in anharmonic bosonic impurity systems. For illustration, we consider the simplest noninteracting systems, with focus on the strikingly different characteristics between the bosonic and fermionic scenarios.