Quantum Monte Carlo Simulation of Generalized Kitaev Models

TL;DR

This paper introduces a phase pinning technique in auxiliary field quantum Monte Carlo to mitigate the negative sign problem in generalized Kitaev models, enabling detailed study of their thermodynamic and dynamical properties.

Contribution

The authors develop a phase pinning approach that improves the average sign in Monte Carlo simulations of Kitaev models, facilitating exploration of their finite-temperature behaviors.

Findings

Enhanced average sign in Monte Carlo simulations.

Finite temperature properties of ordered and spin-liquid phases.

Successful application to the Kitaev-Heisenberg model.

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.