Quantum critical scaling of fidelity in BCS-like model

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.

26 pages, 30 figures. Added a table summarizing results. Additional comments in figures captions. Clarified some arguments. Added citations. Corrected typos

References in corpus (1)

• Quantum critical scaling of the geometric tensors

Cited by in corpus (3)

• Exact results for fidelity susceptibility of the quantum Ising model: The interplay between parity, system size, and magnetic field
• Numerical studies of ground state fidelity of the Bose-Hubbard model
• Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition