Precision thermodynamics of the strongly interacting Fermi gas in two dimensions

TL;DR

This work tackles the two-dimensional BCS-BEC crossover in the strongly interacting regime by employing canonical-ensemble auxiliary-field quantum Monte Carlo on a lattice and performing continuous-time and continuum-limit extrapolations. The authors compute the condensate fraction, spin susceptibility, energy equation of state, Tan’s contact, and the free-energy staggering gap to map thermodynamics across the crossover, identifying a substantial pseudogap where pairing persists above the superfluid transition temperature $T_c$; notable is the use of continuum-limit AFMC to produce controlled, benchmarkable results, including $T^*$ estimates that relate pairing correlations to the two-body binding energy. The findings provide quantitative benchmarks for experiments and illuminate how high-temperature pairing manifests in 2D Fermi gases, with implications for understanding pseudogap physics and the nature of 2D superfluidity. The work also outlines future directions, such as spectral-function analyses and exploring spin-imbalanced or spin-orbit-coupled regimes, to further elucidate the 2D BCS-BEC landscape.

Abstract

The two-species cold atomic Fermi gas with attractive short-range interactions in two spatial dimensions undergoes a Bardeen-Cooper-Schrieffer (BCS) to a Bose-Einstein Condensate (BEC) crossover as a function of $\ln (k_F a)$, where $a$ is the scattering length. However, the nature of this crossover in the strong coupling regime $\ln(k_F a) \sim 1$ remains poorly understood. In this work we use canonical-ensemble auxiliary-field quantum Monte Carlo methods on discrete lattices to calculate several thermodynamical quantities in the strongly interacting regime, and eliminate systematic errors by extrapolating to continuous time and taking the continuum limit. In particular, we present results for the condensate fraction, spin susceptibility, contact, energy equation of state, and the free energy staggering gap. We identify signatures of a pseudogap regime, in which pairing correlations survive above the critical temperature for superfluidity, in the spin susceptibility and in the free energy staggering gap. These results can be used as a benchmark for future experiments.

Figures (9)

• Figure 1: Continuous time extrapolations for the spin susceptibility $\chi/\chi_0$ at different temperatures for $\ln(k_F a) =1.3$ and $N=114$ particles.
• Figure 2: Continuum limit extrapolations for the spin susceptibility $\chi/\chi_0$ at different temperatures for $\ln(k_F a) =1.3$ and $N=114$ particles.
• Figure 3: Condensate fraction $n_0=\lambda_{\rm max}/(N/2)$ as a function of temperature for different coupling strengths in the crossover regime. We find that above $T_c$, the condensate fraction decreases with increasing particle number, indicating the absence of a condensate in the thermodynamic limit. Below $T_c$, the condensate fraction converges to the thermodynamic limit. The condensate fraction increases as $\ln(k_F a)$ decreases towards $1.0$.
• Figure 4: Spin susceptibility vs. temperature for several coupling strengths $\ln(k_F a)$ in the crossover regime of the 2D interacting Fermi gas. We find that there is a significant pseudogap regime as $\ln(k_F a)\rightarrow 1.0$, characterized by a suppression of the spin susceptibility in a wide temperature regime. In all cases we find that the spin susceptibility is significantly suppressed in the superfluid phase below $T_c$. For each of the three interaction strengths, the black dashed line indicates the critical temperature $T_c$ determined from the FSS analysis in Ref. Ramachandran2024, with the associated statistical uncertainty shown as a gray band. The pseudogap temperature $T^\star$, marking the upper bound of the pseudogap regime, is shown as a dot-dashed line.
• Figure 5: Spin susceptibility at $\ln(k_F a) = 1.0$ as a function of temperature for $N=114$ particles at different lattice sizes, and in the continuum limit (black circles).