Finite temperature contact for SU(2) fermions trapped in a 1D harmonic confinement

TL;DR

This paper computes the finite-temperature Tan's contact for SU(2) fermions in a 1D harmonic trap, revealing a low-temperature minimum caused by state mixing and maximal entanglement in the unitary regime.

Contribution

It provides an explicit low-temperature formula for the contact and links the minimum to state symmetry mixing and entanglement, extending understanding of contact in trapped fermions.

Findings

Tan's contact exhibits a minimum at very low temperatures.

The minimum is due to mixing of states with different exchange symmetries.

Maximal entanglement entropy occurs in the unitary regime.

Abstract

We calculate the finite-temperature Tan's contact for N SU(2) fermions, characterized by repulsive contact interaction, trapped in a 1D harmonic confinement within a local density approximation on top of a thermodynamic Bethe Ansatz. The Tan's contact for such a system, as in the homogeneous case, displays a minimum at a very low temperature. By means of an exact canonical ensemble calculation for two fermions, we provide an explicit formula for the contact at very low temperatures that reveals that the minimum is due to the mixing of states with different exchange symmetries. In the unitary regime, this symmetry blending corresponds to a maximal entanglement entropy.