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

• URL: http://arxiv.org/abs/2201.09904v2
• Date: Wed, 4 May 2022 18:44:45 GMT
• Title: Quantum orders in the frustrated Ising model on the bathroom tile lattice
• Authors: Sumner N. Hearth, Siddhardh C. Morampudi, Chris R. Laumann
• Abstract summary: We determine the zero and finite temperature phase diagram of the fully frustrated quantum Ising model on the bathroom tile (4-8) lattice. Phase diagram exhibits a wealth of 2+1d physics, including classical Coulomb dimer liquids of both square and triangular lattice types. Results provide a baseline for studying frustrated with D-Wave architecture annealers, where the 4-8 lattice can be embedded naturally without cloning', reducing the number of competing energy scales.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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