Quantum fidelity in the thermodynamic limit

TL;DR

This paper investigates quantum fidelity in large many-body systems, revealing how its behavior near critical points encodes universal information about quantum phase transitions, exemplified through the quantum Ising chain.

Contribution

It provides a general scaling framework for quantum fidelity in the thermodynamic limit and derives a simple expression for the quantum Ising chain.

Findings

Fidelity drops near critical points indicate universal quantum phase transition features

Derived a simple, exact fidelity expression for the quantum Ising chain

Fidelity scaling reveals critical behavior in many-body quantum systems

Abstract

We study quantum fidelity, the overlap between two ground states of a many-body system, focusing on the thermodynamic regime. We show how drop of fidelity near a critical point encodes universal information about a quantum phase transition. Our general scaling results are illustrated in the quantum Ising chain for which a remarkably simple expression for fidelity is found.