Extended Quantum Dimer Model and novel valence-bond phases

TL;DR

This paper extends the quantum dimer model to demonstrate multiple exotic valence-bond phases and explores phase transitions, revealing complex ordering phenomena and the role of quantum fluctuations in degeneracy lifting.

Contribution

It introduces a concrete extended quantum dimer model exhibiting multiple exotic valence-bond phases and analyzes phase transitions and degeneracy resolution.

Findings

Identifies three exotic valence-bond phases: herringbone, checkerboard, and dimer smectic.

Shows a first-order phase transition between staggered and herringbone valence-bond solids.

Demonstrates how quantum fluctuations resolve degeneracy in the dimer smectic phase.

Abstract

We extend the quantum dimer model (QDM) introduced by Rokhsar and Kivelson so as to construct a concrete example of the model which exhibits the first-order phase transition between different valence-bond solids suggested recently by Batista and Trugman and look for the possibility of other exotic dimer states. We show that our model contains three exotic valence-bond phases (herringbone, checkerboard and dimer smectic) in the ground-state phase diagram and that it realizes the phase transition from the staggered valence-bond solid to the herringbone one. The checkerboard phase has four-fold rotational symmetry, while the dimer smectic, in the absence of quantum fluctuations, has massive degeneracy originating from partial ordering only in one of the two spatial directions. A resonance process involving three dimers resolves this massive degeneracy and dimer smectic gets ordered (order from disorder).