StableLinearAlgebra.jl
Documentation for StableLinearAlgebra.jl.
This package exports an LDR matrix factorization type for square matrices, along with a corresponding collection of functions for calculating numerically stable matrix products and matrix inverses. The methods exported by the package are essential for implementing a determinant quantum Monte Carlo (DQMC) code for simulating interacting itinerant electrons on a lattice.
A very similar Julia package implementing and exporting many of the same algorithms is StableDQMC.jl.
Installation
To install StableLinearAlgebra.jl run following in the Julia REPL:
julia> ]
pkg> add StableLinearAlgebraReferences
- [1]
- C. Bauer. Fast and stable determinant quantum Monte Carlo. SciPost Physics Core 2, 011 (2020).
- [2]
- J. Gubernatis, N. Kawashima and P. Werner. Quantum Monte Carlo Methods (Cambridge University Press, 2016).
- [3]
- E. Loh Jr and J. Gubernatis. Stable numerical simulations of models of interacting electrons in condensed matter physics. Electronic Phase Transitions 32, 177–235 (1992).
- [4]
- E. Loh, J. Gubernatis, R. Scalettar, S. White, D. Scalapino and R. Sugar. Numerical stability and the sign problem in the determinant quantum Monte Carlo method. International Journal of Modern Physics C 16, 1319–1327 (2005).
- [5]
- S. R. White, D. J. Scalapino, R. L. Sugar, E. Loh, J. E. Gubernatis and R. T. Scalettar. Numerical study of the two-dimensional Hubbard model. Physical Review B 40, 506 (1989).
- [6]
- F. F. Assaad. Quantum Monte Carlo methods on lattices: The determinantal approach. Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms 10, 99–147 (2002).
- [7]
- C.-C. Chang, S. Gogolenko, J. Perez, Z. Bai and R. T. Scalettar. Recent advances in determinant quantum Monte Carlo. Philosophical Magazine 95, 1260–1281 (2015).