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arXiv:2508.16725 · SciPost Physics

Unnecessary quantum criticality in $SU (3)$ kagome magnets

Yunchao Zhang, Xue-Yang Song, T. Senthil

Published Mar 11, 2026• 1 citation
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Abstract

Algebraic/Dirac spin liquids (DSLs) are a class of critical quantum ground states that do not have a quasi-particle description. DSLs and related spin liquid phases often arise in strongly frustrated quantum spin systems, in which strong correlations and quantum fluctuations among constituent spins persist down to zero temperature. In this work, we analyze Mott insulating phases of SU(3) S U ( 3 ) fermions on a kagome lattice which may realize a DSL phase, described at low energies by (2 + 1)d ( 2 + 1 ) d quantum electrodynamics (QED _3 3 ) with N_f=6 N f = 6 Dirac fermions. By analyzing the action of physical symmetries on the operators of the QED _3 3 theory, we conclude that the low energy DSL is a quantum critical point that can be accessed by tuning a single microscopic parameter. Aided by the emergent symmetry and anomalies of the low energy effective theory, we conjecture and present supporting arguments that the SU(3) S U ( 3 ) Kagome magnet DSL is an unnecessary quantum critical point, lying completely within a single phase.

DOI
10.21468/scipostphys.20.3.082

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Unnecessary quantum criticality in SU(3)SU (3)SU(3) kagome magnets
Algebraic/Dirac spin liquids (DSLs) are a class of critical quantum ground states that do not have a quasi-particle description. DSLs and related spin liquid phases often arise in strongly frustrated quantum spin systems, in which strong correlations and quantum fluctuations among constituent spins persist down to zero temperature. In this work, we analyze Mott insulating phases of SU(3) S U ( 3 ) fermions on a kagome lattice which may realize a DSL phase, described at low energies by (2 + 1)d ( 2 + 1 ) d quantum electrodynamics (QED _3 3 ) with N_f=6 N f = 6 Dirac fermions. By analyzing the action of physical symmetries on the operators of the QED _3 3 theory, we conclude that the low energy DSL is a quantum critical point that can be accessed by tuning a single microscopic parameter. Aided by the emergent symmetry and anomalies of the low energy effective theory, we conjecture and present supporting arguments that the SU(3) S U ( 3 ) Kagome magnet DSL is an unnecessary quantum critical point, lying completely within a single phase.
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.
The interplay of symmetry and topology has been at the forefront of recent progress in quantum matter.Here, we uncover an unexpected connection between band topology and the description of competing orders in a quantum magnet.Specifically, we show that aspects of band topology protected by crystalline symmetries determine key properties of the Dirac spin liquid (DSL), which can be defined on the honeycomb, square, triangular, and kagome lattices.At low energies, the DSL on all of these lattices is described by an emergent quantum electrodynamics (QED 3 ) with N f ¼ 4 flavors of Dirac fermions coupled to a Uð1Þ gauge field.However, the symmetry properties of the magnetic monopoles, an important class of critical degrees of freedom, behave very differently on different lattices.In particular, we show that the lattice momentum and angular momentum of monopoles can be determined from the charge (or Wannier) centers of the corresponding spinon insulator.We also show that for DSLs on bipartite lattices, there always exists a monopole that transforms trivially under all microscopic symmetries owing to the existence of a parent SUð2Þ gauge theory.We connect our results to generalized Lieb-Schultz-Mattis theorems and also derive the time-reversal and reflection properties of monopoles.Our results indicate that recent insights into free-fermion band topology can also guide the description of strongly correlated quantum matter.
Abstract Quantum magnets provide the simplest example of strongly interacting quantum matter, yet they continue to resist a comprehensive understanding above one spatial dimension. We explore a promising framework in two dimensions, the Dirac spin liquid (DSL) — quantum electrodynamics (QED 3 ) with 4 Dirac fermions coupled to photons. Importantly, its excitations include magnetic monopoles that drive confinement. We address previously open key questions — the symmetry actions on monopoles on square, honeycomb, triangular and kagome lattices. The stability of the DSL is enhanced on triangular and kagome lattices compared to bipartite (square and honeycomb) lattices. We obtain the universal signatures of the DSL on triangular and kagome lattices, including those of monopole excitations, as a guide to numerics and experiments on existing materials. Even when unstable, the DSL helps unify and organize the plethora of ordered phases in correlated two-dimensional materials.
We explore the Dirac spin liquid (DSL) as a candidate for the ground state of the Mott insulating phase of fermions with six flavors on the kagome lattice, particularly focusing on realizations using 173Yb^{173}\mathrm{Yb}173Yb atoms in optical lattices. Using mean-field theory and variational Monte Carlo simulations, we demonstrate that the DSL has the lowest variational energy among SU(6) symmetry-preserving trial wave functions with a periodicity of a 12-site unit cell, as well as uniform chiral states with larger unit cells. It remains a local minimum even when small second-nearest neighbor and ring-exchange interactions are introduced. To characterize the DSL, we calculate the static and dynamic structure factor of the Gutzwiller projected wave function and compare it with mean-field calculations. The static structure factor shows triangular-shaped plateaus around the K\mathrm{K}K points in the extended Brillouin zone, with small peaks at the corners of these plateaus. The dynamical structure factor consists of a gapless continuum of fractionalized excitations. Our study also presents several complementary results, including bounds for the ground-state energy, methods for calculating three-site ring-exchange expectations in the projective mean field, the boundary of ferromagnetic states, and the nontopological nature of flat bands in the DSL band structure.
There is growing evidence from both experiment and numerical studies that low half-odd integer quantum spins on a kagome lattice with predominant antiferromagnetic near-neighbor interactions do not order magnetically or break lattice symmetries even at temperatures much lower than the exchange interaction strength. Moreover, there appears to be a plethora of low-energy excitations, predominantly singlets but also spin carrying, which suggests that the putative underlying quantum spin liquid is a gapless ``critical spin liquid'' rather than a gapped spin liquid with topological order. Here, we develop an effective field theory approach for the spin-12\frac{1}{2}21​ Heisenberg model with easy-plane anisotropy on the kagome lattice. By employing a vortex duality transformation, followed by a fermionization and flux smearing, we obtain access to a gapless yet stable critical spin liquid phase, which is described by (2+1)(2+1)(2+1)-dimensional quantum electrodynamics (QED3)({\mathrm{QED}}_{3})(QED3​) with an emergent SU(8) flavor symmetry. The specific heat, thermal conductivity, and dynamical structure factor are extracted from the effective field theory, and contrasted with other theoretical approaches to the kagome antiferromagnet.
A complicating factor in the realization and observation of quantum spin liquids in materials is the ubiquitous presence of other degrees of freedom, in particular lattice distortion modes (phonons). These provide additional routes for relieving magnetic frustration, thereby possibly destabilizing spin-liquid ground states. In this work, we focus on triangular-lattice Heisenberg antiferromagnets, where recent numerical evidence suggests the presence of an extended U(1) Dirac spin liquid phase which is described by compact quantum electrodynamics in 2+1 dimensions (QED3_33​), featuring gapless spinons and monopoles as gauge excitations, and believed to flow to a strongly-coupled fixed point with conformal symmetry. Using complementary perturbation theory and scaling arguments, we show that a symmetry-allowed coupling between (classical) finite-wavevector lattice distortions and monopole operators of the U(1) Dirac spin liquid generally induces a spin-Peierls instability towards a (confining) 12-site valence-bond solid state. We support our theoretical analysis with state-of-the-art density matrix renormalization group simulations. Away from the limit of static distortions, we demonstrate that the phonon energy gap establishes a parameter regime where the spin liquid is expected to be stable, and show that the monopole-lattice coupling leads to softening of the phonon in analogy to the Kohn anomaly. We discuss the applicability of our results to similar systems, in particular the Dirac spin liquid on the Kagome lattice.