Lower and upper bounds on the fidelity susceptibility

TL;DR

This paper establishes bounds on fidelity susceptibility using thermodynamic quantities and demonstrates their effectiveness through exactly solvable models, revealing its relation to thermodynamic susceptibility near critical points.

Contribution

It introduces bounds on fidelity susceptibility in terms of thermodynamic quantities and validates them with exactly solvable many-particle models.

Findings

Bounds are tight and useful for critical behavior analysis.

Fidelity susceptibility and thermodynamic susceptibility are equivalent in divergent regimes.

Validated bounds with models like Dicke superradiance and Kondo.

Abstract

We derive upper and lower bounds on the fidelity susceptibility in terms of macroscopic thermodynamical quantities, like susceptibilities and thermal average values. The quality of the bounds is checked by the exact expressions for a single spin in an external magnetic field. Their usefulness is illustrated by two examples of many-particle models which are exactly solved in the thermodynamic limit: the Dicke superradiance model and the single impurity Kondo model. It is shown that as far as divergent behavior is considered, the fidelity susceptibility and the thermodynamic susceptibility are equivalent for a large class of models exhibiting critical behavior.