The algebraic spin liquid in the SU(6) Heisenberg model on the kagome lattice

TL;DR

This paper investigates the Dirac spin liquid as a potential ground state for the SU(6) Heisenberg model on the kagome lattice, demonstrating its energetic favorability and characteristic excitations through theoretical and numerical methods.

Contribution

It introduces a comprehensive analysis of the Dirac spin liquid in the SU(6) kagome model, including variational energy comparisons, structure factor calculations, and stability assessments with additional interactions.

Findings

DSL has the lowest variational energy among SU(6) states.

Static structure factor shows characteristic plateaus and peaks.

Dynamical structure factor reveals a gapless continuum of excitations.

Abstract

We explore the Dirac spin liquid (DSL) as a candidate for the ground state of the Mott insulating phase of fermions with six flavors on the Kagome lattice, particularly focusing on realizations using $^{173}$Yb atoms in optical lattices. Using mean-field theory and variational Monte Carlo simulations, we demonstrate that the Dirac spin liquid (DSL) has the lowest variational energy among SU(6) symmetry-preserving trial wave functions with a periodicity of a 12-site unit cell, as well as uniform chiral states with larger unit cells. It remains a local minimum even when small second-nearest neighbor and ring exchange interactions are introduced. To characterize the DSL, we calculate the static and dynamic structure factor of the Gutzwiller projected wavefunction and compare it with mean-field calculations. The static structure factor shows triangular-shaped plateaus around the $\mathrm{K}$ points in the extended Brillouin zone, with small peaks at the corners of these plateaus. The dynamical structure factor consists of a gapless continuum of fractionalized excitations. Our study also presents several complementary results, including bounds for the ground state energy, methods for calculating three-site ring exchange expectations in the projective mean field, the boundary of ferromagnetic states, and the non-topological nature of flat bands in the DSL band structure.