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arXiv · 2603.15745

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

Atanu Maity·Andreas Feuerpfeil·Ronny Thomale·Subir Sachdev·Yasir Iqbal
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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) $π$-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 Néel 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.

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Atanu Maity, Andreas Feuerpfeil, Ronny Thomale, Subir Sachdev, Yasir Iqbal. 2026-03-16. Unified gauge-theory description of quantum spin liquids on square-based frustrated lattices. https://arxiv.org/abs/2603.15745

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