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

TL;DR

This study uses large-scale, exact numerical methods to map the finite-temperature phase diagram and properties of the 2D Fermi gas across different interaction regimes, revealing detailed behaviors of pairing and contact with temperature.

Contribution

It provides the first systematic, numerically exact analysis of the BKT transition and temperature-dependent properties in the 2D Fermi gas across BCS to BEC regimes.

Findings

Finite-temperature phase diagram of BKT transition mapped.

Non-monotonic temperature dependence of contact observed.

Accurate characterization of pairing wavefunctions and momentum distributions.

Abstract

We perform large-scale, numerically exact 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 from above.