Resonating plaquette phases in large spin cold atom systems

TL;DR

This paper explores the phase diagram of large spin cold atom systems, revealing a gapped quantum phase with a resonating plaquette state and a classical critical line, using a novel gauge field formalism.

Contribution

It introduces a gauge field formalism and duality transformation to analyze the SU(4) resonating plaquette state in three-dimensional cold atom systems, highlighting the gapped nature of the phase diagram.

Findings

System is generally gapped due to topological defects

A critical line exists in the classical plaquette system

Quantum wavefunction corresponds to a plaquette liquid phase

Abstract

Large spin cold atom systems can exhibit novel magnetic properties which do not appear in usual spin-1/2 systems. We investigate the SU(4) resonating plaquette state in the three dimensional cubic optical lattice with spin-3/2 cold fermions. A novel gauge field formalism is constructed to describe the Rokhsar-Kivelson type of Hamiltonian and a duality transformation is used to study the phase diagram. Due to the proliferation of topological defects, the system is generally gapped for the whole phase diagram of the quantum model, which agrees with the recent numerical studies. A critical line is found for the classical plaquette system, which also corresponds to a quantum many-body wavefunction in a "plaquette liquid phase".