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 optimized. As a result, we can reach temperature scales well below the magnetic scale. Here, we show how to generalize this algorithm to spin-Peierls systems. In contrast to exact diagonalization 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 nonfrustrated spin systems.

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• Frustrated magnetism
• Spin-phonon coupling
• Strongly correlated systems
• Heisenberg model
• Kitaev-Heisenberg model
• Quantum Monte Carlo