Schur complement solver for Quantum Monte-Carlo simulations of strongly interacting fermions
arXiv:1803.05478 · doi:10.1016/j.cpc.2018.10.023
Abstract
We present a non-iterative solver based on the Schur complement method for sparse linear systems of special form which appear in Quantum Monte-Carlo (QMC) simulations of strongly interacting fermions on the lattice. While the number of floating-point operations for this solver scales as the cube of the number of lattice sites, for practically relevant lattice sizes it is still significantly faster than iterative solvers such as the Conjugate Gradient method in the regime of strong inter-fermion interactions, for example, in the vicinity of quantum phase transitions. The speed-up is even more dramatic for the solution of multiple linear systems with different right-hand sides. We present benchmark results for QMC simulations of the tight-binding models on the hexagonal graphene lattice with on-site (Hubbard) and non-local (Coulomb) interactions, and demonstrate the potential for further speed-up using GPU.
23 pages, 5 figures. Journal version: accepted for publication in Computer Physics Communications
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- Numerical evidence of conformal phase transition in graphene with long-range interactions
- Avoiding Ergodicity Problems in Lattice Discretizations of the Hubbard Model
- Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses
- Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo
- Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice
- Instanton gas approach to the Hubbard model
- Minimal Autocorrelation in Hybrid Monte Carlo simulations using Exact Fourier Acceleration