Mixed-state fidelity susceptibility through iterated commutator series expansion

TL;DR

This paper introduces a perturbative method to compute mixed-state fidelity susceptibility using an iterated commutator series, simplifying calculations for models with algebraic symmetries.

Contribution

It provides an analytical expansion for MFS involving higher commutators, enabling easier evaluation for models with algebraic symmetry properties.

Findings

Expansion simplifies calculations for models with Lie algebra symmetries

Method separates isothermal susceptibility from noncommutative contributions

Closed-form expressions obtained for models with finite-dimensional algebraic symmetry

Abstract

We present a perturbative approach to the problem of computation of mixed-state fidelity susceptibility (MFS) for thermal states. The mathematical techniques used provides an analytical expression for the MFS as a formal expansion in terms of the thermodynamic mean values of successively higher commutators of the Hamiltonian with the operator involved through the control parameter. That expression is naturally divided into two parts: the usual isothermal susceptibility and a constituent in the form of an infinite series of thermodynamic mean values which encodes the noncommutativity in the problem. If the symmetry properties of the Hamiltonian are given in terms of the generators of some (finite dimensional) algebra, the obtained expansion may be evaluated in a closed form. This issue is tested on several popular models, for which it is shown that the calculations are much simpler if they are based on the properties from the representation theory of the Heisenberg or SU(1, 1) Lie algebra.