Classification of spin-$1/2$ fermionic quantum spin liquids on the trillium lattice

TL;DR

This paper classifies symmetric fermionic quantum spin liquids on the trillium lattice, identifying specific gapless states with unique band structures and symmetry protections, advancing understanding of frustrated quantum magnetism.

Contribution

It provides the first classification of symmetric $ ext{Z}_2$ and $ ext{U}(1)$ quantum spin liquids on the trillium lattice using PSG analysis, revealing a limited set of states due to non-symmorphic symmetries.

Findings

Identified 2 $ ext{Z}_2$ and 1 $ ext{U}(1)$ spin liquids on the trillium lattice.

All states are gapless at saddle points, with distinct nodal and Fermi surface features.

Discovered a stable, symmetry-protected gapless nodal star in one $ ext{Z}_2$ state.

Abstract

We study fermionic quantum spin liquids (QSLs) on the three-dimensonal trillium lattice of corner-sharing triangles. We are motivated by recent experimental and theoretical investigations that have explored various classical and quantum spin liquid states on similar networks of triangular motifs with strong geometric frustration. Using the framework of Projective Symmetry Groups (PSG), we obtain a classification of all symmetric $\mathsf{Z}_2$ and $\mathsf{U}(1)$ QSLs on the trillium lattice. We find 2 $\mathsf{Z}_2$ spin-liquids, and a single $\mathsf{U}(1)$ spin-liquid which is proximate to one of the $\mathsf{Z}_2$ states. The small number of solutions reflects the constraints imposed by the two non-symmorphic symmetries in the space group of trillium. Using self-consistency conditions of the mean-field equations, we obtain the spinon band-structure and spin structure factors corresponding to these states. All three of our spin liquids are gapless at their saddle points: the $\mathsf{Z}_2$ QSLs are both nodal, while the $\mathsf{U}(1)$ case hosting a spinon Fermi surface. One of our $\mathsf{Z}_2$ spin liquids hosts a stable gapless nodal star, that is protected by projective symmetries against additions of further neighbour terms in the mean field ansatz. We comment on directions for further work.