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

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.

14 pages, 20 figures

References in corpus (4)

• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Simulating the Shastry-Sutherland Ising Model using Quantum Annealing
• Evidence of columnar order in the fully frustrated transverse field Ising model on the square lattice

Cited by in corpus (2)

• Simulating the Transverse Field Ising Model on the Kagome Lattice using a Programmable Quantum Annealer
• Primary and Secondary Order Parameters in the Fully Frustrated Transverse Field Ising Model on the Square Lattice