Quantum Monte Carlo with the Langevin Equation: Coupled Bose-Fermi Systems

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 Ns3 for on-site interactions and Ns4 for long range electron-phonon coupling, even on rather small lattice sizes. © 2019 IOP Publishing Ltd. All rights reserved.