Quantum orders in the frustrated Ising model on the bathroom tile lattice

TL;DR

This paper maps out the complex phase diagram of the fully frustrated quantum Ising model on the bathroom tile lattice, revealing diverse classical and quantum phases, and discusses implications for quantum annealing hardware.

Contribution

It provides the first comprehensive phase diagram of the frustrated Ising model on the 4-8 lattice using multiple theoretical and computational methods.

Findings

Identification of classical Coulomb dimer liquids on square and triangular lattices.

Discovery of quantum order-by-disorder phases breaking various discrete symmetries.

Observation of finite temperature KT phases over certain ordered states.

Abstract

We determine the zero and finite temperature phase diagram of the fully frustrated quantum Ising model on the bathroom tile (4-8) lattice. The phase diagram exhibits a wealth of 2+1d physics, including 1. classical Coulomb dimer liquids of both square and triangular lattice types; 2. quantum order-by-disorder induced phases breaking $\mathbb{Z}_4$, $\mathbb{Z}_6$, and $\mathbb{Z}_8$ symmetries; 3. finite temperature Kosterlitz-Thouless (KT) phases floating over the $\mathbb{Z}_6$ and $\mathbb{Z}_8$ orders; and, 4. staircases of (in)-commensurate symmetry breaking phases at intermediate coupling. We establish this elaborate phase diagram using a combination of dimer model mapping, perturbation theory, Landau analysis and Stochastic Series Expansion Quantum Monte Carlo (QMC-SSE). Our results provide a baseline for studying frustrated magnetism with D-Wave architecture annealers, where the 4-8 lattice can be embedded naturally without `cloning', reducing the number of competing energy scales. Simulations with the D-Wave 2000Q demonstrate qualitative agreement with the high temperature portion of the phase diagram, but are unable to access the low temperature phases.