Fidelity and criticality of quantum Ising chain with long-range interactions

TL;DR

This paper investigates the critical behavior of a long-range quantum Ising chain with algebraically decaying interactions, using fidelity susceptibility to analyze how critical exponents vary with interaction range.

Contribution

It provides detailed numerical analysis of critical exponents and critical points for the long-range quantum Ising chain, confirming and extending recent renormalization group results.

Findings

Critical exponents vary monotonously with interaction decay parameter α.

Critical values are determined for 1.8 ≤ α ≤ 3.

Fidelity susceptibility effectively captures phase transition properties.

Abstract

We study the criticality of long-range quantum ferromagnetic Ising chain with algebraically decaying interactions $1/r^{\alpha}$ via the fidelity susceptibility based on the exact diagonalization and the density matrix renormalization group techniques. We find that critical exponents change monotonously from the mean-field universality class to the short-range Ising universality class for intermediate $\alpha$, which are consistent with recent results obtained from renormalization group. In addition, we determine the critical values for $1.8 \le \alpha \le 3$ from the finite-size scaling of the fidelity susceptibility. Our work provides very nice numerical data from the fidelity susceptibility for the quantum long-range ferromagnetic Ising chain.