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Abstract
We describe the algorithmic details and a performance evaluation of a Langevin approach to a strongly interacting electron-phonon system, and show it has a near linear scaling with lattice size N s . Many of the limitations of previous attempts to employ such methods to condensed matter lattice Hamiltonians are absent. In particular, the iterative linear algebra solution remains well behaved at strong coupling and low temperatures. The use of Fourier Acceleration is crucial for efficiency, and its use makes the method competitive with the widely-used local update methods, which scale as \({N}_{s}^{3}\) for on-site interactions and \({N}_{s}^{4}\) for long range electron-phonon coupling, even on rather small lattice sizes.
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Details
1 Université Côte d’Azur, INPHYNI, CNRS, 0600 Nice, France; MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Unit, 117542 Singapore; Centre for Quantum Technologies, National University of Singapore, 117542 Singapore; Beijing Computational Science Research Center, Beijing 100193, China
2 Department of Physics, University of California, Davis, California 95616, USA