Chiral spin liquid phase in an optical lattice at mean-field level

TL;DR

This paper demonstrates the theoretical possibility of realizing a chiral spin liquid phase in an optical lattice with synthetic gauge flux, using slave-rotor and spinon mean-field theories, highlighting the role of gauge flux and magnetic frustration.

Contribution

It introduces a theoretical framework for realizing and analyzing the chiral spin liquid phase in optical lattices with synthetic gauge flux using two mean-field approaches.

Findings

CSL phase appears at intermediate Hubbard interaction regime.

Strong interactions lead to an effective spin model with four-spin interactions.

Both mean-field methods produce consistent phase diagrams supporting CSL stability.

Abstract

We study an optical Raman square lattice with $\mathrm{U}(1)$ synthetic gauge flux to show chiral spin liquid (CSL) phase for cold atoms based on slave-rotor theory and spinon mean-field theory, respectively. An effective U($1$) gauge flux generated by Raman potentials plays a major role in realizing the CSL phase. By using slave-rotor techniques we find CSL phase at intermediate on-site Fermi Hubbard interacting regime. For the strong interacting regime we derive an effective spin model including up to the four spin interactions. By spinon mean-field analysis it is shown that CSL phase is stabilized in the case of strong magnetic frustration. The two mean-field approximation methods give consistent phase diagrams and provide qualitative numerical evidence of the CSL phase.