Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition

TL;DR

This paper reveals the fundamental link between ground-state fidelity and energy derivatives in quantum systems, showing their equivalence in detecting quantum phase transitions across various models.

Contribution

It establishes a general theoretical connection between fidelity and energy derivatives, enhancing understanding of quantum phase transition signatures.

Findings

Fidelity and energy derivatives are intrinsically related in identifying QPTs.

Different singularity and scaling behaviors of fidelity are explained generally.

Illustrated with multiple quantum spin models exhibiting various QPTs.

Abstract

The notion of fidelity in quantum information science has been recently applied to analyze quantum phase transitions from the viewpoint of the ground state (GS) overlap for various many-body systems. In this work, we unveil the intrinsic relation between the GS fidelity and the derivatives of GS energy and find that they play equivalent role in identifying the quantum phase transition. The general connection between the two approaches enables us to understand the different singularity and scaling behaviors of fidelity exhibited in various systems on general grounds. Our general conclusions are illustrated via several quantum spin models which exhibit different kinds of QPTs.