Quantum Monte Carlo Simulation of Generalized Kitaev Models

Abstract

Frustrated spin systems generically suffer from the negative sign problem inherent to Monte Carlo methods. Since the severity of this problem is formulation dependent, optimization strategies can be put forward. We introduce a phase pinning approach in the realm of the auxiliary field quantum Monte Carlo algorithm. If we can find an anti-unitary operator that commutes with the one body Hamiltonian coupled to the auxiliary field, then the phase of the action is pinned to $0$ and $\pi$. For generalized Kitaev models, we can successfully apply this strategy and observe a remarkable improvement of the average sign. We use this method to study thermodynamical and dynamical properties of the Kitaev-Heisenberg model down to temperatures corresponding to half of the exchange coupling constant. Our dynamical data reveals finite temperature properties of ordered and spin-liquid phases inherent to this model.

5 pages, 5 figures, supplemental material

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• Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models
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• Ground-State Phase Diagram of the Kitaev-Heisenberg Model on a Three-dimensional Hyperhoneycomb Lattice
• Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time
• Quantum spin models of commensurate $p$-wave magnets
• A quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field
• Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models
• Scale-invariant magnetic anisotropy in $\alpha$-RuCl${}_3$: A quantum Monte Carlo study
• Phase diagram of the Kitaev-Hubbard model: ${\mathbb{Z}}_2$ slave-spin and QMC approaches
• Negative sign free formulations of generalized Kitaev models with higher symmetries
• Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers