Finite temperature fermion Monte Carlo simulations of frustrated spin-Peierls systems

TL;DR

This paper extends fermion Monte Carlo simulations to frustrated spin-Peierls systems, enabling exploration of phonon effects on magnetic frustration at low temperatures with manageable sign problems.

Contribution

The authors generalize an auxiliary-field quantum Monte Carlo algorithm to include phonons in frustrated spin systems, maintaining efficiency and manageable sign issues.

Findings

Able to simulate lower temperatures in frustrated systems

Inclusion of phonons does not worsen the sign problem in the Kitaev-Heisenberg model

Provides insights into phonon-magnetic frustration interplay

Abstract

The Abrikosov fermion representation of the spin-1/2 degree of freedom allows for auxiliary-field quantum Monte Carlo simulations of frustrated spin systems. This approach provides a manifold of equivalent actions over which the negative sign problem can be optimised. As a result, we can reach temperature scales well below the magnetic scale. Here, we show how to generalise this algorithm to spin-Peierls systems. In contrast to exact diagonalisation approaches, Monte Carlo methods are not Hilbert space bound such that the computational effort per sweep remains invariant when adding phonons. However, the computational effort required to generate independent configurations increases in the presence of phonons. We also show that, for the specific case of the Kitaev-Heisenberg model, the inclusion of phonons does not render the negative sign problem more severe. This new algorithm hence allows us to investigate the interplay between phonon degrees of freedom and magnetic frustration. We present results for frustrated and non-frustrated spin systems.