Classification and properties of quantum spin liquids on the hyperhoneycomb lattice

TL;DR

This paper classifies symmetric quantum spin liquids on the hyperhoneycomb lattice, identifying promising candidates with nodal-line spinon Fermi surfaces relevant to pressurized iridates, advancing understanding of quantum spin liquids in Kitaev materials.

Contribution

It systematically classifies symmetric quantum spin liquids on the hyperhoneycomb lattice and identifies key candidates near the Kitaev model ground state.

Findings

Identified 8 promising $U(1)$ spin liquid candidates.

All candidates support nodal-line-shaped spinon Fermi surfaces.

Provided physical property analysis of the candidate states.

Abstract

The family of "Kitaev materials" provides an ideal platform to study quantum spin liquids and their neighboring magnetic orders. Motivated by the possibility of a quantum spin liquid ground state in pressurized hyperhoneycomb iridate $\beta$-Li$_2$IrO$_3$, we systematically classify and study symmetric quantum spin liquids on the hyperhoneycomb lattice, using the Abrikosov-fermion representation. Among the 176 symmetric $U(1)$ spin liquids (and 160 $Z_2$ spin liquids), we identify 8 "root" $U(1)$ spin liquids in proximity to the ground state of the solvable Kitave model on hyperhonecyomb lattices. These 8 states are promising candidates for possible $U(1)$ spin liquid ground states in pressurized $\beta$-Li$_2$IrO$_3$. We further discuss physical properties of these 8 $U(1)$ spin liquid candidates, and show that they all support nodal-line-shaped spinon Fermi surfaces.