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

2009/07/31 by Stephen Powell, J. T. Chalker · 26 citations
Physics and Astronomy · #Boson #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Coulomb #Dimer #Electron #Gauge theory #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum mechanics #Quantum phase transition #Quantum phases #Quantum, superfluid, helium dynamics #Superfluidity #Theoretical physics #Vortex #Wigner crystal #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevb.80.134413

published in Physical Review B 80(13) (American Physical Society) · 15 pages, 5 figures; v2: added appendix

openalex publication_date 2009/10/15 · arxiv created 2009/10/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Disorder and interactions in Aharonov-Bohm cages
• Evidence for Deconfined Quantum Criticality in a Two-Dimensional Heisenberg Model with Four-Spin Interactions
• Superfluid-insulator transitions of bosons on the kagome lattice at noninteger fillings
• An attempt to extend the statistical theory of perfect solutions
• Gauge Theory Picture of an Ordering Transition in a Dimer Model
• Vortex pinning and non-Hermitian quantum mechanics
• Classical to quantum mappings for geometrically frustrated systems: Spin-ice in a [100] field
• Three-Dimensional Kasteleyn Transition: Spin Ice in a [100] Field
• SU(2)-Invariant Continuum Theory for an Unconventional Phase Transition in a Three-Dimensional Classical Dimer Model
• Putting competing orders in their place near the Mott transition
• Quantum orders and symmetric spin liquids

Cited by

• Higgs transitions of spin ice
• Confinement of monopoles and scaling theory near unconventional critical points
• Critical behavior in the cubic dimer model at nonzero monomer density