Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases

TL;DR

This paper reviews a generalized Bose-Fermi mapping and a strong coupling ansatz wavefunction for 1D strongly interacting spinor quantum gases, enabling easier analysis of their physical properties and dynamics.

Contribution

It introduces a novel generalized mapping and an ansatz wavefunction specifically designed for strongly interacting 1D spinor quantum gases, facilitating analytical and computational studies.

Findings

Mapping charge to a spinless Fermi gas and spin to a spin chain simplifies analysis.

The ansatz wavefunction allows calculation of collective excitations and quench dynamics.

The approach enables perturbative calculations in strongly interacting regimes.

Abstract

Quantum many-body systems in one dimension (1D) exhibit some peculiar properties. In this article, we review some of our work on strongly interacting 1D spinor quantum gas. First, we discuss a generalized Bose-Fermi mapping that maps the charge degrees of freedom to a spinless Fermi gas and the spin degrees of freedom to a spin chain model. This also maps the strongly interacting system into a weakly interacting one, which is amenable for perturbative calculations. Next, based on this mapping, we construct an ansatz wavefunction for the strongly interacting system, using which many physical quantities can be conveniently calculated. We showcase the usage of this ansatz wavefunction by considering the collective excitations and quench dynamics of a harmonically trapped system.