Condensate Fraction Scaling and Specific Heat Anomaly around Berezinskii-Kosterlitz-Thouless Transition of Superconductivity and Superfluidity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908376230789120 |
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| author | He, Yuan-Yao |
| author_facet | He, Yuan-Yao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17411 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Condensate Fraction Scaling and Specific Heat Anomaly around Berezinskii-Kosterlitz-Thouless Transition of Superconductivity and Superfluidity He, Yuan-Yao Strongly Correlated Electrons 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. |
| title | Condensate Fraction Scaling and Specific Heat Anomaly around Berezinskii-Kosterlitz-Thouless Transition of Superconductivity and Superfluidity |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2505.17411 |