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arXiv:2204.06146 · Physical review. B./Physical review. B

Multicritical point and unified description of broken-symmetry phases in spin- 12 antiferromagnets on a square lattice

Oğuz Türker, Kun Yang

Published Apr 25, 2022• 4 citations
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Abstract

We show that several distinct broken-symmetry phases in a spin-$\frac{1}{2}$ antiferromagnet on a square lattice with easy-plane anisotropy, including valence bond solid, chiral spin liquid, and the XY-ordered state, can all be accessed by perturbing a multicritical point with two massless Dirac fermions coupled to a level-one Chern-Simons gauge field. This allows for a unified description of these phases, as well as the phase transitions between them. In a specific phase transition, our analysis provides a lattice realization of one of the recently proposed fermion-boson dualities, thus lending support to it. We also briefly discuss the relation between our paper and the long-sought deconfined criticality in such systems.

DOI
10.1103/physrevb.105.155150

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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-12\tfrac{1}{2}21​ Heisenberg antiferromagnets on the square, Shastry-Sutherland, and checkerboard lattices can realize a single unified quantum phase: a gapless Z2\mathbb{Z}_2Z2​ 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) πππ-flux parent state and are governed by the same gauge theory, QED3_33​ 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.