Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain

TL;DR

This study investigates the quantum phase transitions in a long-range antiferromagnetic Ising chain using fidelity susceptibility, revealing universal critical exponents and a phase diagram for various interaction ranges.

Contribution

It provides the first comprehensive analysis of the phase diagram and critical behavior of the quantum long-range Ising chain using fidelity susceptibility and DMRG methods.

Findings

Critical adiabatic dimension μ=2 for all α>0

Correlation length exponent ν=1 for all α>0

Monotonous change of critical point h_c with α

Abstract

We study the fidelity susceptibility of quantum antiferromagnetic Ising chain with a long-range power law interaction $1/r^{\alpha}$ using the large-scale density matrix renormalization group method. We find that the critical adiabatic dimension $\mu=2$ and the critical exponent of the correlation length $\nu=1$ for arbitrary $\alpha>0$, indicating all quantum phase transitions are second-order Ising transitions. In addition, we numerically determine the complete phase diagram for $0 < \alpha \le 3$ from the data collapse of the fidelity susceptibility and show that the critical point $h_c$ changes monotonously with respect to $\alpha$. This work will shed light on the nature of phase transitions in the quantum long-range antiferromagnetic Ising chain from a quantum information perspective.