Characterization of quantum spin liquids and their spinon band structures via functional renormalization

TL;DR

This paper introduces a combined PFFRG and mean-field approach to systematically determine spinon band structures in quantum spin liquids, providing insights into their low-energy excitations and emergent phenomena.

Contribution

It develops a novel method integrating PFFRG with a self-consistent mean-field scheme to analyze spinon excitations beyond traditional mean-field approximations.

Findings

Identified a SU(2) π-flux state with Dirac spinons in the J1-J2 model.

Discovered a gapless Z2 spin liquid with a small Fermi surface on the kagome lattice.

Provided detailed spinon band structures for candidate spin-liquid systems.

Abstract

We combine the pseudofermion functional renormalization group (PFFRG) method with a self-consistent Fock-like mean-field scheme to calculate low-energy effective theories for emergent spinon excitations in spin-1/2 quantum spin liquids. Using effective spin interactions from PFFRG as an input for the Fock equation and allowing for the most general types of free spinon ans\"atze as classified by the projective symmetry group (PSG) method, we are able to systematically determine spinon band structures for spin-liquid candidate systems beyond mean-field theory. We apply this approach to the antiferromagnetic $J_1$-$J_2$ Heisenberg model on the square lattice and to the antiferromagnetic nearest-neighbor Heisenberg model on the kagome lattice. For the $J_1$-$J_2$ model, we find that in the regime of maximal frustration a SU(2) $\pi$-flux state with Dirac spinons yields the largest mean-field amplitudes. For the kagome model, we identify a gapless $\mathbb{Z}_2$ spin liquid with a small circular spinon Fermi surface and approximate Dirac-cones at low but finite energies.