Exact results for fidelity susceptibility of the quantum Ising model: The interplay between parity, system size, and magnetic field

TL;DR

This paper derives exact formulas for the fidelity susceptibility of quantum Ising chains, revealing how parity, system size, and magnetic field influence quantum phase transitions and correcting previous misunderstandings.

Contribution

It provides the first exact closed-form expressions for the fidelity susceptibility and the energy gap in quantum Ising models, clarifying the role of parity and system size.

Findings

Exact formulas for fidelity susceptibility in quantum Ising chains.

Identification of ground state parity based on the energy gap.

Exponential dependence of the gap on system size and correlation length.

Abstract

We derive an exact closed-form expression for fidelity susceptibility of even- and odd-sized quantum Ising chains in the transverse field. To this aim, we diagonalize the Ising Hamiltonian and study the gap between its positive and negative parity subspaces. We derive an exact closed-form expression for the gap and use it to identify the parity of the ground state. We point out misunderstanding in some of the former studies of fidelity susceptibility and discuss its consequences. Last but not least, we rigorously analyze the properties of the gap. For example, we derive analytical expressions showing its exponential dependence on the ratio between the system size and the correlation length.