Columnar dimer and plaquette resonating valence bond states of the quantum dimer model

TL;DR

This study investigates the ground state of the quantum dimer model on square lattices, finding no evidence of a dimer liquid phase and identifying a transition from a columnar to a plaquette RVB state with specific finite-size scaling behaviors.

Contribution

The paper provides a detailed finite-size analysis of the quantum dimer model, revealing a transition to a plaquette RVB state and clarifying the phase diagram without a dimer liquid phase.

Findings

No evidence of a dimer liquid state in finite regions.

Identification of a transition to a plaquette RVB state at negative V/J.

The energy gap vanishes as a power law with system size.

Abstract

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 $L\times L$, where $L\leq 8$, 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 identified to be the plaquette resonating valence bond (RVB) state. The energy gap of this state vanishes as a power law of $L$. It exhibits columnar dimer order, but has disorder {\it within} the dimer columns. This state persists up to $V/J<1$, and the system changes to a dimer liquid state only at $V/J=1$.