Dynamical dimer correlations at bipartite and non-bipartite Rokhsar-Kivelson points

TL;DR

This paper investigates the dynamical dimer correlations at Rokhsar-Kivelson points across different lattices, revealing gapless modes, dispersion relations, and spectral features through a novel stochastic simulation approach.

Contribution

It introduces a stochastic analytical continuation method to compute dynamical correlations in quantum dimer models at Rokhsar-Kivelson points, providing new insights into their spectral properties.

Findings

Confirmed analytical predictions of soft modes on square lattice

Identified a single soft mode with quadratic then linear dispersion on cubic lattice

Discovered a rich spectral structure and quasiparticle peaks in the triangular lattice

Abstract

We determine the dynamical dimer correlation functions of quantum dimer models at the Rokhsar-Kivelson point on the bipartite square and cubic lattices and the non-bipartite triangular lattice. Based on an algorithmic idea by Henley, we simulate a stochastic process of classical dimer configurations in continuous time and perform a stochastic analytical continuation to obtain the dynamical correlations in momentum space and the frequency domain. This approach allows us to observe directly the dispersion relations and the evolution of the spectral intensity within the Brillouin zone beyond the single-mode approximation. On the square lattice, we confirm analytical predictions related to soft modes close to the wavevectors (pi,pi) and (pi,0) and further reveal the existence of shadow bands close to the wavevector (0,0). On the cubic lattice the spectrum is also gapless but here only a single soft mode at (pi,pi,pi) is found, as predicted by the single mode approximation. The soft mode has a quadratic dispersion at very long wavelength, but crosses over to a linear behavior very rapidly. We believe this to be the remnant of the linearly dispersing "photon" of the Coulomb phase. Finally the triangular lattice is in a fully gapped liquid phase where the bottom of the dimer spectrum exhibits a rich structure. At the M point the gap is minimal and the spectral response is dominated by a sharp quasiparticle peak. On the other hand, at the X point the spectral function is much broader. We sketch a possible explanation based on the crossing of the coherent dimer excitations into the two-vison continuum.