Bilayer Coulomb phase of two dimensional dimer models: Absence of power-law columnar order

Abstract

We study the fully-packed dimer model on the bilayer square lattice with fugacity equal to $z$ ($1$) for inter-layer (intra-layer) dimers, and intra-layer interaction $V$ between neighbouring parallel dimers on any elementary plaquette in either layer. For a range of not-too-large $z>0$ and repulsive interactions $0<V<V_s$ (with $V_s\approx 2.1$), we demonstrate the existence of a {\em bilayer Coulomb phase} with purely dipolar two-point functions, {\em i.e.}, without the power-law columnar order that characterizes the usual Coulomb phase of square and honeycomb lattice dimer models. The transition line $z_c(V)$ separating this bilayer Coulomb phase from a large-$z$ disordered phase is argued to be in the inverted Kosterlitz-Thouless universality class. Additionally, we argue for the possibility of a tricritical point at which the bilayer Coulomb phase, the large-$z$ disordered phase and the large-$V$ staggered phase meet in the large-$z$, large-$V$ part of the phase diagram. In contrast, for the attractive case with $V_{cb}<V\le 0$ ($V_{cb}\approx -1.2$), we argue that any $z>0$ destroys the power-law correlations of the $z=0$ decoupled layers, and leads immediately to a short-range correlated state, albeit with a slow crossover for small $|V|$. For $V_c<V<V_{cb}$ ($V_c\approx -1.55$), we predict that any small nonzero $z$ immediately gives rise to long-range {\em bilayer columnar order} although the $z=0$ decoupled layers remain power-law correlated in this regime; this implies a non-monotonic $z$ dependence of the columnar order parameter for fixed $V$ in this regime. This bilayer columnar ordered state is separated from the large-$z$ disordered state by a line of Ashkin-Teller transitions $z_{\mathrm{AT}}(V)$.

Minor changes from v2 in response to copy editor's comments. Closely matches published version

References in corpus (8)

• Interacting classical dimers on the square lattice
• Classical dimers with aligning interactions on the square lattice
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• Unconventional continuous phase transition in a three dimensional dimer model
• Correlations and confinement in non-planar two-dimensional dimer models
• Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system
• Interacting double dimer model on the square lattice
• Classical dimer model with anisotropic interactions on the square lattice

Cited by in corpus (9)

• Emergent Fracton Dynamics in a Non-Planar Dimer Model
• Dulmage-Mendelsohn percolation: Geometry of maximally-packed dimer models and topologically-protected zero modes on site-diluted bipartite lattices
• Asymptotic Freedom at the Berezinskii-Kosterlitz-Thouless Transition without Fine-Tuning Using a Qubit Regularization
• Ashkin-Teller phase transition and multicritical behavior in a classical monomer-dimer model
• Quantum Kasteleyn transition
• Derivation of field theory for the classical dimer model using bosonization
• Phases of the hard-plate lattice gas on a three-dimensional cubic lattice
• Spontaneous layering and power-law order in the three-dimensional fully-packed hard-plate lattice gas
• Dynamic scaling near the Kasteleyn transition in spin ice: critical relaxation of monopoles and strings following a field quench