Height-conserving quantum dimer models

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.

5+14 pages, 4+10 figures

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• Re-entrance effect in the high-temperature critical phase of the quantum dimer model on the square lattice
• Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models
• Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice
• Exploring the topological sector optimization on quantum computers
• Cubic* criticality emerging from a quantum loop model on triangular lattice
• Models of interacting bosons with exact ground states: a unified approach
• Classical fully-packed loop model with attractive interactions on the square lattice
• Jordan-Wigner composite-fermion liquids in 2D quantum spin-ice
• Accessing Excitation of Many-body Systems via Single-Mode Approximation within Quantum Monte Carlo Simulations
• Doped resonating-valence-bond states: Robustness of the spin-ice phases in three-dimensional Rydberg arrays