Exact pairing correlations in one-dimensional trapped fermions with stochastic mean-field wave-functions

TL;DR

This paper investigates the thermodynamic properties and pairing correlations of one-dimensional trapped fermions using an exact stochastic mean-field approach, revealing transitions to BCS-like states and superfluid behavior.

Contribution

It introduces an exact stochastic mean-field method to analyze pairing and superfluidity in 1D trapped fermions, providing new insights into their quantum correlations.

Findings

Transition to quasi-BCS state with Cooper-like correlations

Algebraic long-range order observed in trapped systems

Superfluid component with quantized circulation identified in rotating traps

Abstract

The canonical thermodynamic properties of a one-dimensional system of interacting spin-1/2 fermions with an attractive zero-range pseudo-potential are investigated within an exact approach. The density operator is evaluated as the statistical average of dyadics formed from a stochastic mean-field propagation of independent Slater determinants. For an harmonically trapped Fermi gas and for fermions confined in a 1D-like torus, we observe the transition to a quasi-BCS state with Cooper-like momentum correlations and an algebraic long-range order. For few trapped fermions in a rotating torus, a dominant superfluid component with quantized circulation can be isolated.