We introduce the quantum dimer-pentamer model (QDPM) on the square lattice. This model is a generalization of the square-lattice quantum dimer model as its configuration space comprises fully packed hard-core dimer coverings as well as dimer configurations containing pentamers, where four dimers touch a vertex. Thus in the QDPM, the fully packed, hard-core constraint of the quantum dimer model is relaxed such that the local dimer number at each vertex is fixed modulo 3, resulting in an exact local ${Z}_{3}$ gauge symmetry. We construct a local Hamiltonian for which the Rokhsar-Kivelson (RK) equal superposition state is the exact ground state and has a ninefold topological degeneracy on the torus. Using Monte Carlo calculations, we find no spontaneous symmetry breaking in the RK wave function and that its dimer-dimer correlation function decays exponentially. By doping the QDPM RK state with a pair of monomers, we demonstrate that ${Z}_{3}$ electric charges are deconfined. Additionally, we introduce a ${Z}_{3}$ magnetic string operator that we find decays exponentially and shows no signatures of magnetic vortex condensation. These numerical results suggest that the ground state of the QDPM is a dimer liquid with ${Z}_{3}$ topological order.We introduce the quantum dimer-pentamer model (QDPM) on the square lattice. This model is a generalization of the square-lattice quantum dimer model as its configuration space comprises fully packed hard-core dimer coverings as well as dimer configurations containing pentamers, where four dimers touch a vertex. Thus in the QDPM, the fully packed, hard-core constraint of the quantum dimer model is relaxed such that the local dimer number at each vertex is fixed modulo 3, resulting in an exact local ${Z}_{3}$ gauge symmetry. We construct a local Hamiltonian for which the Rokhsar-Kivelson (RK) equal superposition state is the exact ground state and has a ninefold topological degeneracy on the torus. Using Monte Carlo calculations, we find no spontaneous symmetry breaking in the RK wave function and that its dimer-dimer correlation function decays exponentially. By doping the QDPM RK state with a pair of monomers, we demonstrate that ${Z}_{3}$ electric charges are deconfined. Additionally, we introduce a ${Z}_{3}$ magnetic string operator that we find decays exponentially and shows no signatures of magnetic vortex condensation. These numerical results suggest that the ground state of the QDPM is a dimer liquid with ${Z}_{3}$ topological order.

arXiv:1704.02063Physical review. B./Physical review. BNov 27, 20173 citations

Quantum Dimer Model: Phase Diagrams

Garry Goldstein, Claudio Chamon, Claudio Castelnovo

Bulletin of the American Physical SocietyMar 14, 20160 citations

Quantum Dimer Models and Exotic Orders

K. S. Raman, Eduardo Fradkin, Roderich Moessner +2 more

arXiv:0809.3050NATO science for peace and security series. B, Physics and biophysicsJan 1, 20080 citations

Quantum dimer model with extensive ground-state entropy on the kagome lattice

Grégoire Misguich, Didina Serban, Vincent Pasquier

We introduce a quantum dimer model on the kagome lattice with kinetic terms allowing from three to six dimers to resonate around hexagons. Unlike the models studied previously, the different resonance loops appear with different signs (given by the parity of the number of dimers involved). These signs naturally appear when performing the lowest-order overlap expansion (Rokhsar and Kivelson 1988) of the Heisenberg model. We demonstrate that the quantum dimer model has an extensive zero-temperature entropy and has very short-range dimer-dimer correlations. We discuss the possible relevance of this kind of quantum dimer liquid to the physics of the spin- $\frac{1}{2}$ Heisenberg model on the kagome lattice.We introduce a quantum dimer model on the kagome lattice with kinetic terms allowing from three to six dimers to resonate around hexagons. Unlike the models studied previously, the different resonance loops appear with different signs (given by the parity of the number of dimers involved). These signs naturally appear when performing the lowest-order overlap expansion (Rokhsar and Kivelson 1988) of the Heisenberg model. We demonstrate that the quantum dimer model has an extensive zero-temperature entropy and has very short-range dimer-dimer correlations. We discuss the possible relevance of this kind of quantum dimer liquid to the physics of the spin-$\frac{1}{2}$ Heisenberg model on the kagome lattice.

arXiv:cond-mat/0302152Physical review. B, Condensed matterJun 10, 200361 citations

Dimer Smectic in Extended Quantum Dimer Model -approach from pseudo S=1 Hamiltonian-

Kouki Nakata, Keisuke Totsuka

We extend Quantum Dimer Model (QDM) introduced by Rokhsar and Kivelson in such a way that the model includes resonance processes on larger loops. The strategy is to first construct a pseudo spin Hamiltonian which is defined not by the S =1/2 but by the S=1 representation and then establish the correspondence between the pseudo-spin-1 configurations and those of dimers. The standard QDM keeps only the lowest resonance processes for pairs of parallel dimers and its validity in describing the realistic spin systems is not obvious. Our extended QDM (EQDM) improves this point and contains a novel resonance term, which is equivalent to two successive actions of the familiar parallel dimer resonance. For a certain choice of the coupling constants, our model exhibits three exotic valence-bond phases (herringbone, checkerboard and 'dimer smectic') in the ground state, which meet at a triple point. The checkerboard phase has four-fold rotational symmetry, while the dimer smectic is characterized by partial ordering only in one of the two directions. In the dimer smectic phase, we investigate the dimer-dimer correlation by using an analogy to random walks.We extend Quantum Dimer Model (QDM) introduced by Rokhsar and Kivelson in such a way that the model includes resonance processes on larger loops. The strategy is to first construct a pseudo spin Hamiltonian which is defined not by the S =1/2 but by the S=1 representation and then establish the correspondence between the pseudo-spin-1 configurations and those of dimers. The standard QDM keeps only the lowest resonance processes for pairs of parallel dimers and its validity in describing the realistic spin systems is not obvious. Our extended QDM (EQDM) improves this point and contains a novel resonance term, which is equivalent to two successive actions of the familiar parallel dimer resonance. For a certain choice of the coupling constants, our model exhibits three exotic valence-bond phases (herringbone, checkerboard and 'dimer smectic') in the ground state, which meet at a triple point. The checkerboard phase has four-fold rotational symmetry, while the dimer smectic is characterized by partial ordering only in one of the two directions. In the dimer smectic phase, we investigate the dimer-dimer correlation by using an analogy to random walks.

arXiv:1004.1040Apr 7, 20100 citations

A round-trip from spin to quantum dimer models

Matthieu Mambrini, Fabien Alet, Sylvain Capponi

Bulletin of the American Physical SocietyFeb 29, 20120 citations

{Z}_{3}

gauge symmetry. We construct a local Hamiltonian for which the Rokhsar-Kivelson (RK) equal superposition state is the exact ground state and has a ninefold topological degeneracy on the torus. Using Monte Carlo calculations, we find no spontaneous symmetry breaking in the RK wave function and that its dimer-dimer correlation function decays exponentially. By doping the QDPM RK state with a pair of monomers, we demonstrate that

{Z}_{3}

electric charges are deconfined. Additionally, we introduce a

{Z}_{3}

magnetic string operator that we find decays exponentially and shows no signatures of magnetic vortex condensation. These numerical results suggest that the ground state of the QDPM is a dimer liquid with

{Z}_{3}

topological order.

\frac{1}{2}

Heisenberg model on the kagome lattice.