Fidelity approach to quantum phase transitions in quantum Ising model

TL;DR

This paper explores the use of fidelity, the overlap between ground states, to analyze quantum phase transitions in the 1D quantum Ising model, providing analytical expressions and insights into transition dynamics.

Contribution

It introduces analytical formulas for fidelity in the quantum Ising model and demonstrates its effectiveness in understanding quantum phase transitions.

Findings

Analytical expressions for fidelity in the 1D quantum Ising model.

Fidelity provides insights into the dynamics of quantum phase transitions.

Role of fidelity in central spin systems is highlighted.

Abstract

Fidelity approach to quantum phase transitions uses the overlap between ground states of the system to gain some information about its quantum phases. Such an overlap is called fidelity. We illustrate how this approach works in the one dimensional quantum Ising model in the transverse field. Several closed-form analytical expressions for fidelity are discussed. An example of what insights fidelity provides into the dynamics of quantum phase transitions is carefully described. The role of fidelity in central spin systems is pointed out.