Quantum critical scaling of fidelity in BCS-like model

TL;DR

This paper investigates how ground-state fidelity scales near quantum critical points in a BCS-like fermionic model, revealing both regular and anomalous scaling behaviors through numerical and analytical methods, including comparisons with spin chain models.

Contribution

The study provides exact diagonalization analysis of fidelity scaling in a BCS-like model, deriving analytical formulas in 1D, and identifying anomalous scaling near multi-critical points.

Findings

Fidelity scaling obeys known laws near regular critical points.

Anomalous scaling occurs near multi-critical points.

Strong fidelity oscillations are observed near certain critical points.

Abstract

We study scaling of the ground-state fidelity in neighborhoods of quantum critical points in a model of interacting spinfull fermions - a BCS-like model. Due to the exact diagonalizability of the model, in one and higher dimensions, scaling of the ground-state fidelity can be analyzed numerically with great accuracy, not only for small systems but also for macroscopic ones, together with the crossover region between them. Additionally, in one-dimensional case we have been able to derive a number of analytical formulae for fidelity and show that they accurately fit our numerical results; these results are reported in the article. Besides regular critical points and their neighborhoods, where well-known scaling laws are obeyed, there is the multi-critical point and critical points in its proximity where anomalous scaling behavior is found. We consider also scaling of fidelity in neighborhoods of critical points where fidelity oscillates strongly as the system size or the chemical potential is varied. Our results for a one-dimensional version of a BCS-like model are compared with those obtained by Rams and Damski in similar studies of a quantum spin chain - an anisotropic XY model in transverse magnetic field.