Exactly solvable model for isospin S=3/2 fermionic atoms on an optical lattice

TL;DR

This paper presents an exact solution for a model describing low-energy behavior of isospin S=3/2 fermionic atoms in a 1D optical lattice, revealing different symmetries depending on band filling.

Contribution

It provides an exact analytical solution for a low-energy effective model of fermionic atoms with isospin S=3/2 on a lattice, identifying symmetry structures at different fillings.

Findings

Exact solution for the model at different fillings.

Identification of symmetry groups: $O(7)\times \mathbb{Z}_2$ and $U(1)\times O(5)\times \mathbb{Z}_2$.

Connection to deformed Gross-Neveu models.

Abstract

We propose an exact solution of a model describing a low energy behavior of cold isospin S=3/2 fermionic atoms on a one-dimensional optical lattice. Depending on the band filling the effective field theory has a form of a deformed Gross-Neveu model with either $O(7)\times \mathbb{Z}_2$ (half filling) or $U(1)\times O(5)\times \mathbb{Z}_2$ symmetry.