Numerical methods and analytic results for one-dimensional strongly interacting spinor gases

TL;DR

This paper develops a new computational approach for analyzing correlation functions in one-dimensional strongly interacting spinor gases, enabling studies of larger systems and revealing novel temperature-dependent phenomena.

Contribution

A novel, efficient method for calculating correlation functions in strongly interacting 1D spinor gases, scalable to larger particle numbers and applicable to equilibrium and nonequilibrium states.

Findings

The momentum distribution narrows with increasing temperature.

Derived determinant representations for correlators in the spin incoherent regime.

New phenomena observed in static and dynamic properties of the system.

Abstract

One of quantum physics' fundamental, but largely unsolved, problems is the computation of the correlation functions in many-body systems. In this paper we address this problem in the case of one-dimensional spinor gases with repulsive contact interactions in the presence of a confining potential. We take advantage of the fact that in the strong coupling limit, the wavefunction factorizes with the charge degrees of freedom expressed as a Slater determinant of spinless fermions and the spin sector described by a spin chain of Sutherland type with exchange coefficients that depend only on the trapping potential. This factorization is also present in the expressions for the correlation functions. Still, analytical and numerical investigations were hindered by the fact that the local exchange coefficients and the charge component of the correlators are expressed as $N-1$ multidimensional integrals, with $N$ the number of particles, which are notoriously hard to compute using conventional methods. We introduce a new approach to calculating these integrals that is extremely simple, scales polynomially with the number of particles, and is several orders of magnitude faster than the previous methods reported in the literature. This allows us to investigate the static and dynamic properties, temperature dependence, and nonequilibrium dynamics for systems with a larger number of particles than previously considered and discover new phenomena. We show that, contrary to natural expectations, the momentum distribution of strongly interacting trapped spinor gases becomes narrower as we increase the temperature and derive simple determinant representations for the correlators in the spin incoherent regime valid for both equilibrium and nonequilibrium situations.