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arXiv:2407.09713 · Physical review. B./Physical review. B

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

Dániel Vörös, Péter Kránitz, Karlo Penc

Published Oct 23, 2024• 0 citations
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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 $^{173}\mathrm{Yb}$ atoms in optical lattices. Using mean-field theory and variational Monte Carlo simulations, we demonstrate that the 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 wave function 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 nontopological nature of flat bands in the DSL band structure.

DOI
10.1103/physrevb.110.144437

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We investigate the extended Heisenberg model on the kagome lattice by using Gutzwiller projected fermionic states and the variational Monte Carlo technique. In particular, when both second- and third-neighbor superexchanges are considered, we find that a gapped spin liquid described by nontrivial magnetic fluxes and long-range chiral-chiral correlations is energetically favored compared to the gapless U(1) Dirac state. Furthermore, the topological Chern number, obtained by integrating the Berry curvature, and the degeneracy of the ground state, by constructing linearly independent states, lead us to identify this flux state as the chiral spin liquid with a C=1/2C=1/2C=1/2 fractionalized Chern number.
The parton approach for quantum spin liquids gives a transparent description of low-energy elementary excitations, e.g., spinons and emergent gauge-field fluctuations. The latter ones are directly coupled to the hopping/pairing of spinons. By using the fermionic representation of the U(1)U(1)U(1) Dirac state on the kagome lattice and variational Monte Carlo techniques to include the Gutzwiller projection, we analyze the effect of modifying the gauge fields in the spinon kinematics. In particular, we construct low-energy monopole excitations, which are shown to be gapless in the thermodynamic limit. States with a finite number of monopoles or with a finite density of them are also considered, with different patterns of the gauge fluxes. We show that these chiral states are not stabilized in the Heisenberg model with nearest-neighbor superexchange couplings, and the Dirac state corresponds to the lowest-energy ansatz within this family of variational wave functions. Our results support the idea that spinons with a gapless conical spectrum coexist with gapless monopole excitations, even for the spin-1/2 case.