Abstract We analyze a Higgs transition from a U(1) Dirac spin liquid to a gapless ℤ2 spin liquid. This ℤ2 spin liquid is of relevance to the spin S = 1/2 square lattice antiferromagnet, where recent numerical studies have given evidence for such a phase existing in the regime of high frustration between nearest neighbor and next-nearest neighbor antiferromagnetic interactions (the J1-J2 model), appearing in a parameter regime between the vanishing of Néel order and the onset of valence bond solid ordering. The proximate Dirac spin liquid is unstable to monopole proliferation on the square lattice, ultimately leading to Néel or valence bond solid ordering. As such, we conjecture that this Higgs transition describes the critical theory separating the gapless ℤ2 spin liquid of the J1-J2 model from one of the two proximate ordered phases. The transition into the other ordered phase can be described in a unified manner via a transition into an unstable SU(2) spin liquid, which we have analyzed in prior work. By studying the deconfined critical theory separating the U(1) Dirac spin liquid from the gapless ℤ2 spin liquid in a 1/Nf expansion, with Nf proportional to the number of fermions, we find a stable fixed point with an anisotropic spinon dispersion and a dynamical critical exponent z ≠ 1. We analyze the consequences of this anisotropic dispersion by calculating the angular profiles of the equal-time Néel and valence bond solid correlation functions, and we find them to be distinct. We also note the influence of the anisotropy on the scaling dimension of monopoles.
The theory for the vanishing of N\'eel order in the spin
S=1/2 square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model): A gapless spin liquid is present for a narrow window of parameters between the vanishing of the N\'eel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable
Z2 spin liquid with massless Dirac spinon excitations; on the other side of the critical point, the SU(2) spin liquid (the `$\ensuremath{\pi}$-flux' phase) is presumed to be unstable to confinement to the N\'eel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant and weakly breaks the SO(5) symmetry which rotates between the N\'eel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless
Z2 spin liquid; on the other side of the critical point, the U(1) spin liquid (the `staggered flux' phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent $z\ensuremath{\ne}1$, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing
J2/J1: N\'eel, gapless
Z2 spin liquid, and valence bond solid.
We present a fermionic gauge theory for deconfined quantum criticality on the Shastry-Sutherland lattice and reveal its shared low-energy field-theoretic structure with the square lattice. Starting from an SU(2)
π-flux parent state, we construct a continuum theory of Dirac spinons coupled to an SU(2) gauge field and adjoint Higgs fields whose condensates drive transitions to a staggered-flux U(1) spin liquid and a gapless
Z2 Dirac spin liquid. While the Shastry-Sutherland lattice permits additional symmetry-allowed fermion bilinears compared to the square lattice, the quantum field theories are identical up to additional irrelevant terms. Consequently, the Higgs potential structure and the leading low-energy theory coincide with the square-lattice case at the quantum critical point. The SO(5) critical point is expected to realize conformal deconfined criticality: we analyze it in a large flavor expansion, calculate its critical exponents, and identify the Yukawa coupling between the fermions and Higgs fields as the relevant perturbation that destabilizes it, consistent with pseudocritical behavior observed in recent Monte Carlo studies. We show that the emergent SO(5) order parameter acquires a large anomalous dimension at the critical point, leading to strongly enhanced Néel and VBS susceptibilities-a hallmark of fermionic deconfined quantum criticality consistent with numerical studies. Our results place recent numerical evidence for a gapless
Z2 Dirac spin liquid on the Shastry-Sutherland lattice within a controlled field-theoretic framework and demonstrate that fermionic deconfined criticality on the square lattice-including critical exponents and stability-extends to frustrated lattices with reduced symmetry.
Quantum fluctuations of the Néel state of the square lattice antiferromagnet are usually described by a CP 1 theory of bosonic spinons coupled to a U(1) gauge field, and with a global SU(2) spin rotation symmetry.Such a theory also has a confining phase with valence bond solid (VBS) order, and upon including spin-singlet charge-2 Higgs fields, deconfined phases with Z 2 topological order possibly intertwined with discrete broken global symmetries.We present dual theories of the same phases starting from a mean-field theory of fermionic spinons moving in π flux in each square lattice plaquette.Fluctuations about this π-flux state are described by (2 þ 1)-dimensional quantum chromodynamics (QCD 3 ) with a SU(2) gauge group and N f ¼ 2 flavors of massless Dirac fermions.It has recently been argued by Wang et al. [Deconfined Quantum Critical Points: Symmetries and Dualities, Phys. Rev. X 7, 031051 (2017).]that this QCD 3 theory describes the Néel-VBS quantum phase transition.We introduce adjoint Higgs fields in QCD 3 and obtain fermionic dual descriptions of the phases with Z 2 topological order obtained earlier using the bosonic CP 1 theory.We also present a fermionic spinon derivation of the monopole Berry phases in the U(1) gauge theory of the VBS state.The global phase diagram of these phases contains multicritical points, and our results imply new boson-fermion dualities between critical gauge theories of these points.
The
U(1) Dirac spin liquid might realize an exotic phase of matter whose low-energy properties are described by quantum electrodynamics in
2+1 dimensions, where gapless modes exist but spinons and gauge fields are strongly coupled. Its existence was proposed in frustrated Heisenberg models in the presence of frustrating superexchange interactions by the (Abrikosov) fermionic representation of the spin operators [Wen, Phys. Rev. B 65, 165113 (2002)], supplemented by the Gutzwiller projection. Here, we construct charge-
Q monopole excitations in the Heisenberg model on the triangular lattice with nearest-neighbor (
J1) and next-nearest-neighbor (
J2) couplings. In the highly frustrated regime, singlet and triplet monopoles with
Q=1 become gapless in the thermodynamic limit; in addition, the energies for generic
Q agree with field-theoretical predictions, obtained for a large number of gapless fermion modes. Finally, we consider localized gauge excitations, in which magnetic $\ensuremath{\pi}$ fluxes are concentrated in the triangular plaquettes (in analogy with
Z2 visons), showing that these kinds of states do not play a relevant role at low energies. All our findings lend support to a stable
U(1) Dirac spin liquid in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the triangular lattice.
Quantum spin liquids are exotic phases of quantum matter especially pertinent to many modern condensed matter systems. Dirac spin liquids (DSLs) are a class of gapless quantum spin liquids that do not have a quasi-particle description and are potentially realized in a wide variety of spin 1/2 1 / 2 magnetic systems on 2d 2 d lattices. In particular, the DSL in square lattice spin- 1/2 1 / 2 magnets is described at low energies by (2+1)d ( 2 + 1 ) d quantum electrodynamics with N_f=4 N f = 4 flavors of massless Dirac fermions minimally coupled to an emergent U(1) U ( 1 ) gauge field. The existence of a relevant, symmetry-allowed monopole perturbation renders the DSL on the square lattice intrinsically unstable. We argue that the DSL describes a stable continuous phase transition within the familiar Neel phase (or within the Valence Bond Solid (VBS) phase). In other words, the DSL is an ``unnecessary’’ quantum critical point within a single phase of matter. Our result offers a novel view of the square lattice DSL in that the critical spin liquid can exist within either the Neel or VBS state itself, and does not require leaving these conventional states.
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-
21 Heisenberg antiferromagnets on the square, Shastry-Sutherland, and checkerboard lattices can realize a single unified quantum phase: a gapless
Z2 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.