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We study scaling of the ground-state fidelity in neighborhoods of quantumcritical 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 greataccuracy, not only for small systems but also for macroscopic ones, togetherwith the crossover region between them. Additionally, in one-dimensional casewe have been able to derive a number of analytical formulae for fidelity andshow that they accurately fit our numerical results; these results are reportedin the article. Besides regular critical points and their neighborhoods, wherewell-known scaling laws are obeyed, there is the multi-critical point andcritical points in its proximity where anomalous scaling behavior is found. Weconsider also scaling of fidelity in neighborhoods of critical points wherefidelity oscillates strongly as the system size or the chemical potential isvaried. Our results for a one-dimensional version of a BCS-like model arecompared with those obtained by Rams and Damski in similar studies of a quantumspin chain - an anisotropic XY model in transverse magnetic field.

Quantum critical scaling of fidelity in BCS-like model