Stabilizing Canonical-Ensemble Calculations in the Auxiliary-Field Monte Carlo Method
arXiv:1402.3585 · doi:10.1016/j.cpc.2014.09.002
Abstract
Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the auxiliary-field Monte Carlo (AFMC) method, low-temperature or large-model-space calculations require numerically stabilized matrix multiplication. When adapting methods used in the grand-canonical ensemble to the canonical ensemble of fixed particle number, the numerical stabilization increases the number of required floating-point operations for computing observables by a factor of the size of the single-particle model space, and thus can greatly limit the systems that can be studied. We describe an improved method for stabilizing canonical-ensemble calculations in AFMC that exhibits better scaling, and present numerical tests that demonstrate the accuracy and improved performance of the method.
17 pages, 2 figures
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Cited by in corpus (7)
- The contact in the unitary Fermi gas across the superfluid phase transition
- Pairing correlations across the superfluid phase transition in the unitary Fermi gas
- Emergence of a pseudogap in the BCS-BEC crossover
- The pseudogap regime in the unitary Fermi gas
- Finite-size effects in canonical and grand-canonical quantum Monte Carlo simulations for fermions
- A Stable, Recursive Auxiliary Field Quantum Monte Carlo Algorithm in the Canonical Ensemble: Applications to Thermometry and the Hubbard Model
- Sampling Electronic Fock States using Determinant Quantum Monte Carlo