Height-conserving quantum dimer models

TL;DR

This paper introduces a height-conserving quantum dimer model that exhibits Hilbert space fragmentation, maps to the XXZ spin model, and reveals complex phase behavior and glassy phenomena at the Rokhsar-Kivelson point.

Contribution

It proposes a novel height-conserving quantum dimer model with exact mappings to the XXZ model and explores its phase diagram and fragmentation phenomena.

Findings

Hilbert space fragmentation observed in the model

Exact mapping to the XXZ spin model in certain subspaces

Distinct dynamical behaviors across Krylov subspaces at the RK point

Abstract

We propose a height-conserving quantum dimer model (hQDM) such that the lattice sum of its associated height field is conserved, and that it admits a Rokhsar-Kivelson (RK) point. The hQDM with minimal interaction range on the square lattice exhibits Hilbert space fragmentation and maps exactly to the XXZ spin model on the square lattice in certain Krylov subspaces. We obtain the ground-state phase diagram of hQDM via quantum Monte Carlo simulations, and demonstrate that a large portion of it is within the Krylov subspaces which admit the exact mapping to the XXZ model, with dimer ordered phases corresponding to easy-axis and easy-plane spin orders. At the RK point, the apparent dynamical exponents obtained from the single mode approximation and the height correlation function show drastically different behavior across the Krylov subspaces, exemplifying Hilbert space fragmentation and emergent glassy phenomena.