Renormalization, duality, and phase transitions in two- and three-dimensional quantum dimer models

Abstract

We derive an extended lattice gauge theory type action for quantum dimer models and relate it to the height representations of these systems. We examine the system in two and three dimensions and analyze the phase structure in terms of effective theories and duality arguments. For the two-dimensional case we derive the effective potential both at zero and finite temperature. The zero-temperature theory at the Rokhsar-Kivelson (RK) point has a critical point related to the self-dual point of a class of $Z_N$ models in the $N\to \infty$ limit. Two phase transitions featuring a fixed line are shown to appear in the phase diagram, one at zero temperature and at the RK point and another one at finite temperature above the RK point. The latter will be shown to correspond to a Kosterlitz-Thouless (KT) phase transition, while the former will be governed by a KT-like universality class, i.e., sharing many features with a KT transition but actually corresponding to a different universality class. On the other hand, we show that at the RK point no phase transition happens at finite temperature. For the three-dimensional case we derive the corresponding dual gauge theory model at the RK point. We show in this case that at zero temperature a first-order phase transition occurs, while at finite temperatures both first- and second-order phase transitions are possible, depending on the relative values of the couplings involved.

16 pages, 3 figures

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Cited by in corpus (13)

• Symmetry and Topological Order
• The Bond-Algebraic Approach to Dualities
• Phase diagram of an extended classical dimer model
• Eigenstate thermalization hypothesis in quantum dimer models
• Global scheme of sweeping cluster algorithm to sample among topological sectors
• Topological phase transitions in four dimensions
• Re-entrance effect in the high-temperature critical phase of the quantum dimer model on the square lattice
• Fermionic spinon and holon statistics in the pyrochlore quantum spin liquid
• Exact Solution and Correlations of a Quantum Dimer Model on the Checkerboard Lattice
• Robust Topological Degeneracy of Classical Theories
• Topological Phase Transition in a Quasi Two Dimensional Coulomb Gas
• Vison excitations in near-critical quantum dimer models
• Unconventional criticality in $O(D)$-invariant loop-constrained Landau theory