Pairing order and condensate fraction across the BCS-BEC crossover in the two-dimensional attractive Hubbard model
Abstract
We report a systematic study of the superconducting ground state in the two-dimensional attractive Hubbard model, employing the {\it numerically exact} auxiliary-field quantum Monte Carlo method. We focus primarily on the pairing order and condensate fraction across the BCS-BEC crossover. Our numerical calculations cover a broad and physically relevant parameter regime, with the interaction strength U/t=2∼ 12 (where t is the nearest-neighbor hopping amplitude) and fermion density n=0.25∼ 1.0. We systematically characterize the dependence of the pairing order and condensate fraction on both the interaction strength and fermion density, and perform finite-size extrapolations to obtain their thermodynamic-limit values. As complementary quantities, we also provide high-precision numerical results for the double occupancy and total energy. Furthermore, we investigate the effects of next-nearest-neighbor hopping on the superconducting properties of the model. Our results offer a comprehensive set of unbiased numerical data for the attractive Hubbard model, establishing quantitative benchmarks for understanding superconductivity across the BCS-BEC crossover and for validating future theoretical and numerical approaches.
Related
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BibTeX
@misc{du2026pairing,
title = {{Pairing order and condensate fraction across the BCS-BEC crossover in the two-dimensional attractive Hubbard model}},
author = {Hao Du and Qian Sun and Zhuotao Xie and Yuan-Yao He},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06319},
eprint = {2610.06319},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06319},
}
RIS
TY - UNPB
TI - Pairing order and condensate fraction across the BCS-BEC crossover in the two-dimensional attractive Hubbard model
AU - Hao Du
AU - Qian Sun
AU - Zhuotao Xie
AU - Yuan-Yao He
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06319
UR - https://arxiv.org/abs/2610.06319
AB - We report a systematic study of the superconducting ground state in the two-dimensional attractive Hubbard model, employing the {\it numerically exact} auxiliary-field quantum Monte Carlo method. We focus primarily on the pairing order and condensate fraction across the BCS-BEC crossover. Our numerical calculations cover a broad and physically relevant parameter regime, with the interaction strength U/t=2∼ 12 (where t is the nearest-neighbor hopping amplitude) and fermion density n=0.25∼ 1.0. We systematically characterize the dependence of the pairing order and condensate fraction on both the interaction strength and fermion density, and perform finite-size extrapolations to obtain their thermodynamic-limit values. As complementary quantities, we also provide high-precision numerical results for the double occupancy and total energy. Furthermore, we investigate the effects of next-nearest-neighbor hopping on the superconducting properties of the model. Our results offer a comprehensive set of unbiased numerical data for the attractive Hubbard model, establishing quantitative benchmarks for understanding superconductivity across the BCS-BEC crossover and for validating future theoretical and numerical approaches.
ER -