Simulations of Quantum XXZ Models on Two-Dimensional Frustrated Lattices

Abstract

We report recent progress in the study of a particular class of spin 1/2 XXZ model on two-dimensional lattices with frustrated diagonal and unfrustrated off-diagonal interactions. Quantum Monte Carlo simulations can be constructed without a sign problem, however they require non-trivial algorithmic advances in order to combat freezing tendencies. We discuss results obtained using these techniques, in particular the discovery of unusual bulk quantum phases, studies of quantum criticality, and the continuing search for exotic physics in these models.

arXiv comment10 pages, 5 figures. Conference proceedings for Highly Frustrated Magnetism 2006

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• Two-dimensional quantum-spin-1/2 XXZ magnet in zero magnetic field: global thermodynamics from renormalization group theory
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• Quantum disordered ground state for hard-core bosons on the frustrated square lattice
• Anisotropic frustrated Heisenberg model on the honeycomb lattice
• Resummation-based updates for Stochastic Series Expansion Quantum Monte Carlo
• A Large-$S$ Study of Quantum Kagome Ice
• Tuning the disorder of superglasses
• High-field spin-flop state in green dioptase
• Ground state properties of quantum triangular ice
• Quantum triangular ice in the easy-axis ferromagnetic phase
• Quantum disordered ground state for the frustrated square lattice