Unified gauge-theory description of quantum spin liquids on square-based frustrated lattices

TL;DR

This paper presents a unified gauge-theory framework for quantum spin liquids on various frustrated lattices, revealing they can share a common phase despite different lattice symmetries, and linking their properties through emergent gauge theories.

Contribution

It introduces a unified continuum gauge theory description for quantum spin liquids on square, Shastry-Sutherland, and checkerboard lattices, challenging the notion that lattice geometry uniquely determines spin-liquid phases.

Findings

All three lattices host the same gapless $ ext{Z}_2$ Dirac quantum spin liquid.

The spin liquids originate from a common SU(2) $ ext{pi}$-flux parent state.

The phases and transitions can be understood via a unified gauge theory, QED$_3$ with two Dirac fermions.

Abstract

Quantum spin liquids are commonly thought to be highly sensitive to lattice geometry, symmetry, and microscopic exchange patterns, leading to a proliferation of seemingly distinct phases across frustrated magnets. Here, we provide a framework that unifies phases that appear distinct from the viewpoint of this intuition. We postulate that the spin-$\tfrac{1}{2}$ Heisenberg antiferromagnets on the square, Shastry-Sutherland, and checkerboard lattices can realize a single unified quantum phase: a gapless $\mathbb{Z}_2$ Dirac quantum spin liquid, despite their markedly different lattice symmetries. Using a systematic projective symmetry group analysis, we identify a checkerboard spin-liquid state that completes a closed set of adiabatically connected phases linking the well-established square-lattice and Shastry-Sutherland spin liquids. Crucially, we show that this lattice-level unification is mirrored exactly in the continuum description. In all three cases, the spin liquids descend from a common SU(2) $\pi$-flux parent state and are governed by the same gauge theory, QED$_3$ with two Dirac fermion flavors coupled to two adjoint Higgs fields. As a result, we postulate that the surrounding N\'eel and valence-bond-solid phases and their confinement transitions admit a unified interpretation within the framework of deconfined quantum criticality. More broadly, our results suggest that quantum spin liquids are most fundamentally classified not by lattice geometry or microscopic couplings, but by the emergent gauge theory and its Higgs structure. Distinct frustrated lattices can thus host the same quantum phase and exhibit the same confinement mechanisms, despite substantial differences in their microscopic symmetries.