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

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. Other: We thank M. Weber for providing the benchmark data of Fig. 1. We would like to thank W. Brenig, J. Knolle, R. Valenti and J. Willsher for useful discussions. We equally thank E. Huffman and J. Hofmann for discussion on how to generalise the ALF-code to include the spin-Peierls coupling. We gratefully acknowledge the Gauss Centre for Supercomputing e.V. for funding this project by providing computing time on the GCS Supercomputer SUPERMUC-NG at Leibniz Supercomputing, (project number pn73xu) as well as the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the NHR project b133ae. NHR Funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is partially funded by the German Research Foundation (DFG) – 440719683. J.I thanks the DFG for financial support under the AS 120/19-1 grant (Project number, 530989922). T.S thanks the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, project-id 390858490). F.F.A. acknowledge financial support from the DFG under the grant AS 120/16-1 (Project number 493886309) that is part of the collaborative research project SFB Q-M&S funded by the Austrian Science Fund (FWF) F 86. TechnicalInfo: Data set for the paper "Finite temperature fermion Monte Carlo simulations of frustrated spin-Peierls systems" available on https://arxiv.org/abs/2502.06565. The dataset contains results from auxiliary field quantum Monte Carlo for the systems studied in the mentioned paper.