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arXiv:cond-mat/0512579 · Physical Review B

Plaquette phase of the square-lattice quantum dimer model: Quantum Monte Carlo calculations

Olav F. Syljuåsen

Published Jun 13, 2006• 58 citations
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Abstract

The plaquette phase of the square-lattice quantum dimer model is studied using a continuous-time reptation quantum Monte Carlo method for lattices of sizes up to $48\ifmmode\times\else\texttimes\fi{}48$ sites. We determine the location of the phase transition between the columnar and plaquette phases to occur at ${V}_{c}∕J=0.60\ifmmode\pm\else\textpm\fi{}0.05$ which is significantly larger than inferred from previous exact diagonalization studies on smaller lattices. Off diagonal correlation functions are obtained. They exhibit long-range order in the plaquette phase but not at the Rokhsar-Kivelson point. We also observe significant finite-size corrections to scaling for the transition between the plaquette phase and the critical resonating valence bond liquid. This study demonstrates the importance of understanding finite-size effects when considering critical properties of the square-lattice quantum dimer model.

DOI
10.1103/physrevb.73.245105

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The plaquette phase of the square-lattice quantum dimer model is studied using a continuous-time reptation quantum Monte Carlo method for lattices of sizes up to 48\ifmmode×\else\texttimes\fi4848\ifmmode\times\else\texttimes\fi{}4848\ifmmode×\else\texttimes\fi48 sites. We determine the location of the phase transition between the columnar and plaquette phases to occur at Vc∕J=0.60\ifmmode±\else\textpm\fi0.05{V}_{c}∕J=0.60\ifmmode\pm\else\textpm\fi{}0.05Vc​∕J=0.60\ifmmode±\else\textpm\fi0.05 which is significantly larger than inferred from previous exact diagonalization studies on smaller lattices. Off diagonal correlation functions are obtained. They exhibit long-range order in the plaquette phase but not at the Rokhsar-Kivelson point. We also observe significant finite-size corrections to scaling for the transition between the plaquette phase and the critical resonating valence bond liquid. This study demonstrates the importance of understanding finite-size effects when considering critical properties of the square-lattice quantum dimer model.
We study the nature of the ground state of the quantum dimer model proposed by Rokhsar and Kivelson by diagonalizing the Hamiltonian of the model on square lattices of size L\ifmmode\times\else\texttimes\fi{}L, where L\ensuremath{\leqslant}8, with periodic boundary conditions. Finite-size scaling studies of the columnar order parameter and the low lying excitation spectrum show no evidence of a dimer liquid state in any finite region of the zero temperature phase diagram. In addition, we find evidence of a transition from the columnar dimer state to an intermediate state at a negative value of V/J. This state is consistent with the plaquette resonating-valence-bond state. The energy gap of this state vanishes as a power law of L. It exhibits columnar dimer order, but has disorder within the dimer columns. This state persists up to V/J1, and the system changes to a dimer liquid state only at V/J=1. \textcopyright{} 1996 The American Physical Society.
We study the nature of the ground state of the quantum dimer model proposed by Rokhsar and Kivelson by diagonalizing the Hamiltonian of the model on square lattices of size L×LL\times LL×L, where L≤8L\leq 8L≤8, with periodic boundary conditions. Finite-size scaling studies of the columnar order parameter and the low lying excitation spectrum show no evidence of a dimer liquid state in any finite region of the zero temperature phase diagram. In addition, we find evidence of a transition from the columnar dimer state to an intermediate state at a negative value of V/JV/JV/J. This state is identified to be the plaquette resonating valence bond (RVB) state. The energy gap of this state vanishes as a power law of LLL. It exhibits columnar dimer order, but has disorder {\it within} the dimer columns. This state persists up to V/J<1V/J<1V/J<1, and the system changes to a dimer liquid state only at V/J=1V/J=1V/J=1.
We revisit the phase diagram of Rokhsar-Kivelson models, which are used in fields such as superconductivity, frustrated magnetism, cold bosons, and the physics of Josephson junction arrays. From an extended height effective theory, we show that one of two simple generic phase diagrams contains a mixed phase that interpolates continuously between columnar and plaquette states. For the square lattice quantum dimer model we present evidence from exact diagonalization and Green's function Monte Carlo techniques that this scenario is realized, by combining an analysis of the excitation gaps of different symmetry sectors with information on plaquette structure factors. This presents a natural framework for resolving the disagreement between previous studies.
We present a quantum Monte Carlo investigation of the finite-temperature phase diagram of the quantum dimer model on the square lattice. We use the sweeping cluster algorithm, which allows the exact implementation of the dimer constraint, supplemented with an equal-time directed loop move that allows sampling the winding sectors. We find a high-temperature critical phase with power-law correlations that extends down to the Rokhsar-Kivelson point, in the vicinity of which a reentrance effect in the lines of constant exponent is found. For small values of the kinetic energy strength, we find finite-temperature transitions to ordered states (columnar and staggered) which match those of interacting classical dimer models.
A family of models is proposed to describe the motion of holes in a fluctuating quantum dimer background on the square lattice. Following Castelnovo et al. [Ann. Phys. (N.Y.) 318, 316 (2005)], a generalized Rokhsar-Kivelson Hamiltonian at finite doping which can be mapped on a doped interacting classical dimer model is constructed. A simple physical extension of this model is also considered. Using numerical computations and simple considerations based on the above exact mapping, we determine the phase diagram of the model showing a number of quantum phases typical of a doped Mott insulator. The two-hole correlation function generically exhibits short-range or long-range algebraic correlations in the solid (columnar) and liquid (critical) phases of the model, respectively. Evidence for an extended region of a doped valence bond solid phase exhibiting holon pairing but no phase separation is given. In contrast, we show that hole deconfinement occurs in the staggered dimer phase.
Using exact diagonalizations and Green's function Monte Carlo simulations, we have studied the zero-temperature properties of the quantum dimer model on the triangular lattice on clusters with up to 588 sites. A detailed comparison of the properties in different topological sectors as a function of the cluster size and for different cluster shapes has allowed us to identify different phases, to show explicitly the presence of topological degeneracy in a phase close to the Rokhsar-Kivelson point, and to understand finite-size effects inside this phase. The nature of the various phases has been further investigated by calculating dimer-dimer correlation functions. The present results confirm and complement the phase diagram proposed by Moessner and Sondhi on the basis of finite-temperature simulations [Phys. Rev. Lett. 86, 1881 (2001)].