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arXiv:cond-mat/0106288 · Physical review. B, Condensed matter

Phase diagram of the hexagonal lattice quantum dimer model

Roderich Moessner, Shivaji L. Sondhi, Premala Chandra

Published Sep 19, 2001• 153 citations
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Abstract

We discuss the phase diagram of the quantum dimer model on the hexagonal (honeycomb) lattice. In addition to the columnar and staggered valence-bond solids which have been discussed in previous work, we establish the existence of a plaquette valence-bond solid. The transition between the plaquette and columnar phases at $v/t=\ensuremath{-}0.2\ifmmode\pm\else\textpm\fi{}0.05$ is argued to be first order. We note that this model should describe valence-bond-dominated phases of frustrated Heisenberg models on the hexagonal lattice and discuss its relation to recent exact diagonalization work by Fouet et al. on the ${J}_{1}\ensuremath{-}{J}_{2}$ model on the same lattice. Our results also shed light on the properties of the transverse field Ising antiferromagnet on the triangular lattice and the classical Ising antiferromagnet on the stacked triangular lattice, which are related to dimer models by duality.

DOI
10.1103/physrevb.64.144416

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We discuss the phase diagram of the quantum dimer model on the hexagonal (honeycomb) lattice. In addition to the columnar and staggered valence-bond solids which have been discussed in previous work, we establish the existence of a plaquette valence-bond solid. The transition between the plaquette and columnar phases at v/t=\ensuremath−0.2\ifmmode±\else\textpm\fi0.05v/t=\ensuremath{-}0.2\ifmmode\pm\else\textpm\fi{}0.05v/t=\ensuremath−0.2\ifmmode±\else\textpm\fi0.05 is argued to be first order. We note that this model should describe valence-bond-dominated phases of frustrated Heisenberg models on the hexagonal lattice and discuss its relation to recent exact diagonalization work by Fouet et al. on the J1\ensuremath−J2{J}_{1}\ensuremath{-}{J}_{2}J1​\ensuremath−J2​ model on the same lattice. Our results also shed light on the properties of the transverse field Ising antiferromagnet on the triangular lattice and the classical Ising antiferromagnet on the stacked triangular lattice, which are related to dimer models by duality.
We present a comprehensive computational study of the phase diagram of the frustrated S=1/2S=1/2S=1/2 Heisenberg antiferromagnet on the honeycomb lattice, with second-nearest (J2)({J}_{2})(J2​) and third-neighbor (J3)({J}_{3})(J3​) couplings. Using a combination of exact diagonalizations (EDs) of the original spin model, of the Hamiltonian projected into the nearest-neighbor short-range valence-bond basis, and of an effective quantum dimer model, as well as a self-consistent cluster mean-field theory, we determine the boundaries of several magnetically ordered phases in the region ${J}_{2},{J}_{3}\ensuremath{\in}[0,1]$, and find a sizable magnetically disordered region in between. We characterize part of this magnetically disordered phase as a plaquette valence-bond crystal phase. At larger J2{J}_{2}J2​, we locate a sizable region in which staggered valence-bond crystal correlations are found to be important, either due to genuine valence-bond crystal (VBC) ordering or as a consequence of magnetically ordered phases, which break lattice rotational symmetry. Furthermore, we find that a particular parameter-free Gutzwiller projected tight-binding wave function has remarkably accurate energies compared to finite-size extrapolated ED energies along the transition line from conventional N\'eel to plaquette VBC phases, a fact that points to possibly interesting critical behavior---such as a deconfined critical point---across this transition. We also comment on the relevance of this spin model to model the spin liquid region found in the half filled Hubbard model on the honeycomb lattice.
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Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin S=1S=1S=1 Heisenberg model on the honeycomb lattice with the antiferromagnetic first- (J1{J}_{1}J1​) and second-neighbor (J2{J}_{2}J2​) interactions ($0.0\ensuremath{\le}{J}_{2}/{J}_{1}\ensuremath{\le}0.5$) by means of density-matrix renormalization group. In the parameter regime ${J}_{2}/{J}_{1}\ensuremath{\lesssim}0.27$, the system sustains a N\'eel antiferromagnetic phase. At the large J2{J}_{2}J2​ side ${J}_{2}/{J}_{1}\ensuremath{\gtrsim}0.32$, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases $0.27\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.32$, we find a nonmagnetic intermediate region with a plaquette valence-bond order. Although our calculations are limited within a six unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this nonmagnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight into the nonmagnetic phases in the spin-1 system by comparing its phase diagram with the spin-1/21/21/2 system.
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