Quantum spin liquids on the diamond lattice

TL;DR

This paper classifies and analyzes various quantum spin liquid states on the diamond lattice, revealing stable gapless phases with nodal loops and connecting some states to topological insulators, advancing understanding of quantum magnetism.

Contribution

It provides a comprehensive PSG classification of symmetric quantum spin liquids on the diamond lattice, identifying new stable gapless phases and linking them to topological insulator models.

Findings

Identified 2 $SU(2)$, 7 $U(1)$, and 8 $bZ_2$ realizable phases.

Discovered stable gapless nodal loop excitations in certain states.

Connected a $U(1)$ spinon Hamiltonian to the Fu-Kane-Mele topological insulator model.

Abstract

We perform a projective symmetry group classification of spin $S=1/2$ symmetric quantum spin liquids with different gauge groups on the diamond lattice. Employing the Abrikosov fermion representation, we obtain $8$ $SU(2)$, $62$ $U(1)$ and $80$ $\mathbb{Z}_{2}$ algebraic PSGs. Constraining these solutions to mean-field parton Ans\"atze with short-range amplitudes, the classification reduces to only $2$ $SU(2)$, $7$ $U(1)$ and $8$ $\mathbb{Z}_{2}$ distinctly realizable phases. We obtain both the singlet and triplet fields for all Ans\"atze, discuss the spinon dispersions, and present the dynamical spin structure factors within a self-consistent treatment of the Heisenberg Hamiltonian with up to third-nearest neighbor couplings. Interestingly, we find that a zero-flux $SU(2)$ state and some descendent $U(1)$ and $\mathbb{Z}_{2}$ states host robust gapless nodal loops in their dispersion spectrum, owing their stability at the mean-field level to the projective implementation of rotoinversion and screw symmetries. A nontrivial connection is drawn between one of our $U(1)$ spinon Hamiltonians (belonging to the nonprojective class) and the Fu-Kane-Mele model for a three-dimensional topological insulator on the diamond lattice. We show that Gutzwiller projection of the 0- and $\pi$-flux $SU(2)$ spin liquids generates long-range N\'eel order.