Two-dimensional Rokhsar-Kivelson (RK) dimer models on bipartite lattices are generally limited to translation-symmetry-broken dimer crystals. We introduce a tensor-product regularization of the dimer Hilbert space that yields a qubit Hamiltonian interpolating from the RK model to the π -flux toric code, thereby accessing a deconfined Z 2 topological liquid. In this framework, the Z 2 liquid descends from a multicritical U ( 1 ) spin liquid through condensation of a charge-2 Higgs field, thus avoiding confinement. Using iDMRG together with low-energy field theory, we determine a phase diagram containing two continuous quantum phase transitions—a 3 D XY * transition between the Z 2 liquid and the columnar/plaquette-VBS, and a quantum Lifshitz transition between two dimer crystals—alongside a first-order transition between the staggered crystal and the Z 2 liquid. Our field theory suggests a deconfined multicritical point described by an Abelian Higgs model with dynamical critical exponent, z = 2 , where the three transitions meet, highlighting the interplay of fractionalization and emergent gauge fluctuations.
We obtain a quantum dimer model (QDM) containing a Rokhsar-Kivelson (RK) point expressed by spin-
21 Heisenberg antiferromagnets on a diamond-like decorated square lattice. This lattice has macroscopically degenerated nonmagnetic ground states, which are equivalent to the Hilbert space of a square-lattice QDM. Then, a square-lattice QDM containing the RK point as a second-order effective Hamiltonian is obtained by introducing further neighbor couplings as perturbation. Our model can provide a new method for the experimental realization of a resonating valence bond state in the QDM.
A highly efficient and simple-to-implement Monte Carlo algorithm is proposed for the evaluation of the Rényi entanglement entropy (REE) of the quantum dimer model (QDM) at the Rokhsar-Kivelson (RK) point. It makes possible the evaluation of REE at the RK point to the thermodynamic limit for a general QDM. We apply the algorithm to a QDM defined on the triangular and the square lattice in two dimensions and the simple and the face centered cubic (fcc) lattice in three dimensions. We find the REE on all these lattices follows perfect linear scaling in the thermodynamic limit, apart from an even-odd oscillation in the case of the square lattice. We also evaluate the topological entanglement entropy (TEE) with both a subtraction and an extrapolation procedure. We find the QDMs on both the triangular and the fcc lattice exhibit robust Z2 topological order. The expected TEE of ln2 is clearly demonstrated in both cases. Our large scale simulation also proves the recently proposed extrapolation procedure in cylindrical geometry to be a highly reliable way to extract the TEE of a topologically ordered system.
We consider a family of generalized Rokhsar-Kivelson (RK) Hamiltonians, which are reverse-engineered to have an arbitrary edge-weighted superposition of dimer coverings as their exact ground state at the RK point. We focus on a quantum dimer model on the triangular lattice, with doubly periodic edge weights. For simplicity we consider a
2×1 periodic model in which all weights are set to one except for a tunable horizontal edge weight labeled
α. We analytically show that the model exhibits a continuous quantum phase transition at
α=3, changing from a topological
Z2 quantum spin liquid (
α<3) to a columnar ordered state (
α>3). The dimer-dimer correlator decays exponentially on both sides of the transition with the correlation length
ξ∝1/∣α−3∣ and as a power-law at criticality. The vison correlator exhibits an exponential decay in the spin liquid phase, but becomes a constant in the ordered phase, which we explain in terms of loop statistics of the double-dimer model. Using finite-size scaling of the vison correlator, we extract critical exponents consistent with the 2D Ising universality class. Additionally, we analytically show that the topological Rényi entropy of order
∞ (topological min-entropy) changes from
log2 for the quantum spin liquid phase
α<3, to
0 for the ordered phase
α>3, thereby analytically confirming the topological nature of the phase transition.
Recently, quantum dimer models have attracted a great deal of interest as a paradigm for the study of exotic quantum phases. Much of this excitement has centered on the claim that a certain class of quantum dimer model can support a quantum
U(1)-liquid phase with deconfined fractional excitations in three dimensions. These fractional monomer excitations are quantum analogs of the magnetic monopoles found in spin ice. In this paper, we use extensive quantum Monte Carlo simulations to establish the ground-state phase diagram of the quantum dimer model on the three-dimensional diamond lattice as a function of the ratio $\ensuremath{\mu}$ of the potential to kinetic-energy terms in the Hamiltonian. We find that, for ${\ensuremath{\mu}}_{c}=0.75\ifmmode\pm\else\textpm\fi{}0.02$, the model undergoes a first-order quantum phase transition from an ordered ``
R state'' into an extended quantum
U(1)-liquid phase, which terminates in a quantum critical Rokhsar-Kivelson (RK) point for $\ensuremath{\mu}=1$. This confirms the published field-theoretical scenario. We present detailed evidence for the existence of the
U(1)-liquid phase and indirect evidence for the existence of its photon and monopole excitations. Simulations are benchmarked against a variety of exact and perturbative results, and a comparison is made of different variational wave functions. We also explore the ergodicity of the quantum dimer model on a diamond lattice within a given flux sector, identifying a new conserved quantity related to transition graphs of dimer configurations. These results complete and extend the previous analysis of O. Sikora et al. [Phys. Rev. Lett. 103, 247001 (2009)].
We study the
n=2 R\'enyi entanglement entropy of the triangular quantum dimer model via Monte Carlo sampling of Rokhsar-Kivelson- (RK-) like ground-state wave functions. Using the construction proposed by Kitaev and Preskill [Phys. Rev. Lett. 96, 110404 (2006)] and an adaptation of the Monte Carlo algorithm described by Hastings et al. [Phys. Rev. Lett. 104, 157201 (2010)], we compute the topological entanglement entropy (TEE) at the RK point $\ensuremath{\gamma}=(1.001\ifmmode\pm\else\textpm\fi{}0.003)\mathrm{ln}2$, confirming earlier results. Additionally, we compute the TEE of the ground state of a generalized RK-like Hamiltonian and demonstrate the universality of TEE over a wide range of parameter values within a topologically ordered phase approaching a quantum phase transition. For system sizes that are accessible numerically, we find that the quantization of TEE depends sensitively on correlations. We characterize corner contributions to the entanglement entropy and show that these are well described by shifts proportional to the number and types of corners in the bipartition.