Emergent SO(5) symmetry at the columnar ordering transition in the classical cubic dimer model

Abstract

The classical cubic-lattice dimer model undergoes an unconventional transition between a columnar crystal and a dimer liquid, in the same universality class as the deconfined quantum critical point in spin-1/2 antiferromagnets but with very different microscopic physics and microscopic symmetries. Using Monte Carlo simulations, we show that this transition has an emergent SO(5) symmetry relating quantities characterizing the two adjacent phases. While the low-temperature phase has a conventional order parameter, the defining property of the Coulomb liquid on the high-temperature side is deconfinement of monomers, and so the SO(5) symmetry relates fundamentally different types of objects. We study linear system sizes up to $L=96$, and find that this symmetry applies with an excellent precision that consistently improves with system size over this range. It is remarkable that SO(5) emerges in a system as basic as the cubic dimer model, with only simple discrete degrees of freedom. Our results are important evidence for the generality of the SO(5) symmetry that has been proposed for the NCCP${}^1$ field theory. We describe a possible interpretation for these results in terms of a consistent hypothesis for the renormalization-group flow structure, allowing for the possibility that SO(5) may ultimately be a near-symmetry rather than an exact one.

5 pages + supplemental material, 9 figures

References in corpus (15)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Coulomb gas transitions in three-dimensional classical dimer models
• Gauge theory picture of an ordering transition in a dimer model
• Unconventional continuous phase transition in a three dimensional dimer model
• Correlations and confinement in non-planar two-dimensional dimer models
• Level spectroscopy in a two-dimensional quantum magnet: Linearly dispersing spinons at the deconfined quantum critical point
• SU(2)-invariant continuum theory for an unconventional phase transition in a three-dimensional classical dimer model
• Classical to quantum mapping for an unconventional phase transition in a three-dimensional classical dimer model
• Correlations and order parameter at a Coulomb-crystal phase transition in a three-dimensional dimer model

Cited by in corpus (43)

• Confinement transition of ${\mathbb{Z}}_2$ gauge theories coupled to massless fermions: emergent QCD${}_3$ and $SO(5)$ symmetry
• Quantum Criticality and Spin Liquid Phase in the Shastry-Sutherland model
• Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions
• Proximate deconfined quantum critical point in SrCu2(BO3)2
• Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet
• Emergence and spontaneous breaking of approximate O(4) symmetry at a weakly first-order deconfined phase transition
• The emergence of gapless quantum spin liquid from deconfined quantum critical point
• Enhanced thermal Hall effect in the square-lattice Néel state
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Phase diagram, symmetry breaking, and critical behavior of three-dimensional lattice multiflavor scalar chromodynamics
• Deconfined criticality and ghost Fermi surfaces at the onset of antiferromagnetism in a metal
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• Building models of topological quantum criticality from pivot Hamiltonians
• Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation
• Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets
• Extracting subleading corrections in entanglement entropy at quantum phase transitions
• Deconfined quantum criticality in spin-1/2 chains with long-range interactions
• Evolution of entanglement entropy at SU($N$) deconfined quantum critical points
• Unconventional U(1) to ${\mathbf{Z}}_{\mathbf{q}}$ cross-over in quantum and classical $\mathbf{q}$-state clock models
• Statistical physics through the lens of real-space mutual information
• Kibble-Zurek mechanism in a one-dimensional incarnation of deconfined quantum critical point
• Fixed point annihilation for a spin in a fluctuating field
• Quantum criticality with emergent symmetry in the extended Shastry-Sutherland model
• Emergent Symmetry in Quantum Phase Transitions: From Deconfined Quantum Critical Point to Gapless Quantum Spin Liquid
• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Quantum criticality of loops with topologically constrained dynamics
• Dual dynamic scaling in deconfined quantum criticality
• Fermion-induced quantum critical point in the Landau-Devonshire model
• Fermion-induced Dynamical Critical Point
• Synchronization transition in the double dimer model on the cubic lattice
• Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
• Fermion enhanced first-order phase transition and chiral Gross-Neveu tricritical point
• The Chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition
• Classical fully-packed loop model with attractive interactions on the square lattice
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Divergence of the Grüneisen ratio at symmetry-enhanced first-order quantum phase transitions
• Critical structure and emergent symmetry of Dirac fermion systems
• Nematic Antiferromagnetism and Deconfined Criticality from the Interplay between Electron-Phonon and Electron-Electron Interactions
• Quantum scaling of the spin lattice relaxation rate in the checkerboard $J$-$Q$ model
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet
• Short-time critical dynamics in the classical cubic dimer model