Condensate Fraction Scaling and Specific Heat Anomaly around Berezinskii-Kosterlitz-Thouless Transition of Superconductivity and Superfluidity

TL;DR

This paper demonstrates that the condensate fraction is an effective and precise tool for characterizing BKT transitions in 2D superconducting and superfluid systems, with improved finite-size scaling analysis and insights into specific heat anomalies.

Contribution

It introduces a novel application of condensate fraction for accurately determining BKT transition points and scaling behavior in large 2D systems using quantum Monte Carlo simulations.

Findings

Condensate fraction exhibits algebraic scaling below BKT transition.

Condensate fraction shows exponential scaling above BKT transition.

Specific heat displays a peak slightly above the BKT transition temperature.

Abstract

Characterizing the superconducting and superfluid transitions in two-dimensional (2D) many-body systems is of broad interest and remains a fundamental issue. In this study, we establish the {\it condensate fraction} as a highly effective tool to achieve that and accordingly propose efficient schemes for accurately determining the transitions, via numerically exact quantum Monte Carlo simulations. Using the 2D attractive Fermi-Hubbard model as a testbed, we access unprecedented system sizes (up to 4096 lattice sites) and perform a comprehensive analysis for the temperature dependence and finite-size scaling of {\it condensate fraction} across the Berezinskii-Kosterlitz-Thouless (BKT) transition. We demonstrate that this quantity exhibits algebraic scaling below the transition and exponential scaling above it, with significantly smaller finite-size effect comparing to the extensively studied on-site pairing correlator. This greatly improves the determination of BKT transition with moderate system sizes. We also extract the finite-size BKT transition temperature from condensate fraction, and confirm its logarithmic correction on system size. Furthermore, we find that the specific heat displays an anomaly, showing a peak at a temperature slightly above BKT transition. Our findings should be generally applicable to 2D fermionic and bosonic systems hosting superconductivity or superfluidity.