Classical to quantum mapping for an unconventional phase transition in a three-dimensional classical dimer model

Abstract

We study the transition between a Coulomb phase and a dimer crystal observed in numerical simulations of the three-dimensional classical dimer model, by mapping it to a quantum model of bosons in two dimensions. The quantum phase transition that results, from a superfluid to a Mott insulator at fractional filling, belongs to a class that cannot be described within the Landau-Ginzburg-Wilson paradigm. Using a second mapping, to a dual model of vortices, we show that the long-wavelength physics near the transition is described by a U(1) gauge theory with SU(2) matter fields.

15 pages, 5 figures; v2: added appendix

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• Emergence and spontaneous breaking of approximate O(4) symmetry at a weakly first-order deconfined phase transition
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• Phase diagram of an extended classical dimer model
• Emergent SO(5) symmetry at the columnar ordering transition in the classical cubic dimer model
• Fragmentation in Frustrated Magnets -- A review
• Scaling dimensions of higher-charge monopoles at deconfined critical points
• Topological aspects of symmetry breaking in triangular-lattice Ising antiferromagnets
• Higgs transitions of spin ice
• Critical behavior in the cubic dimer model at nonzero monomer density
• Monopole holes in a partially ordered spin liquid
• Statistical physics through the lens of real-space mutual information
• Spin-liquid behaviour and the interplay between Pokrovsky-Talapov and Ising criticality in the distorted, triangular-lattice, dipolar Ising antiferromagnet
• Confinement of monopoles and scaling theory near unconventional critical points
• Ferromagnetic Coulomb phase in classical spin ice
• First order phase transitions in the square lattice "easy-plane" J-Q model
• Universal monopole scaling near transitions from the Coulomb phase
• Classical fully-packed loop model with attractive interactions on the square lattice
• Short-time critical dynamics in the classical cubic dimer model
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet