Precision Many-Body Study of the BKT Transition and Temperature-Dependent Properties in the Two-Dimensional Fermi Gas

We perform large-scale, numerically exact Quantum Monte Carlo [1] calculations on the two-dimensional interacting Fermi gas with a contact attraction. Reaching much larger lattice sizes and lower temperatures than previously possible, we determine systematically the finite-temperature phase diagram of the Berezinskii-Kosterlitz-Thouless (BKT) transitions for interaction strengths ranging from BCS to crossover to BEC regimes. The evolutions of the pairing wavefunctions and the fermion and Cooper pair momentum distributions with temperature are accurately characterized. In the crossover regime, we find that the contact has a non-monotonic temperature dependence, first increasing as temperature is lowered, and then showing a slight decline below the BKT transition temperature to approach the ground-state value [2] from above. We also compute the equation of state as a function of interaction strength for various temperatures. We expect that these results will serve as a useful guide for future experiments, and provide unbiased comparison and benchmark for the other analytical and computational studies.

References:

[1] Yuan-Yao He, Hao Shi, Shiwei Zhang, Physical Review Letters. 123, 136402 (2019).

[2] Hao Shi, Simone Chiesa, Shiwei Zhang, Physical Review A 92, 033603 (2015).