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Discrete Hubbard-Stratonovich transformations for systems with orbital degeneracy

O. Gunnarsson, Erik Koch

arXiv:cond-mat/9707035Physics Letters ANov 1, 19976 citations

Flexible class of exact Hubbard-Stratonovich transformations

Seher Karakuzu, Benjamin Cohen-Stead, Cristian D. Batista +2 more

We consider a class of Hubbard-Stratonovich transformations suitable for treating Hubbard interactions in the context of quantum Monte Carlo simulations. A tunable parameter p allows us to continuously vary from a discrete Ising auxiliary field (p=∞) to a compact auxiliary field that couples to electrons sinusoidally (p=0). In tests on the single-band square and triangular Hubbard models, we find that the severity of the sign problem decreases systematically with increasing p. Selecting p finite, however, enables continuous sampling methods such as the Langevin or Hamiltonian Monte Carlo methods. We explore the tradeoffs between various simulation methods through numerical benchmarks.We consider a class of Hubbard-Stratonovich transformations suitable for treating Hubbard interactions in the context of quantum Monte Carlo simulations. A tunable parameter p allows us to continuously vary from a discrete Ising auxiliary field (p=∞) to a compact auxiliary field that couples to electrons sinusoidally (p=0). In tests on the single-band square and triangular Hubbard models, we find that the severity of the sign problem decreases systematically with increasing p. Selecting p finite, however, enables continuous sampling methods such as the Langevin or Hamiltonian Monte Carlo methods. We explore the tradeoffs between various simulation methods through numerical benchmarks.

arXiv:2211.05074Physical review. EMay 4, 20237 citations

Reinvestigation of the sign problem in the two-dimensional Hubbard model

Fakher F. Assaad, Diethelm W�rtz

The European Physical Journal BOct 1, 19907 citations

Numerical studies of the Hubbard model

Anthony John Guttmann, Colin J. Thompson, Sam Y. S. Yang

Nuclear Physics B - Proceedings SupplementsMay 1, 19912 citations

Benchmark study of an auxiliary-field quantum Monte Carlo technique for the Hubbard model with shifted-discrete Hubbard-Stratonovich transformations

Kazuhiro Seki, Sandro Sorella

Within the ground-state auxiliary-field quantum Monte Carlo technique, we introduce discrete Hubbard-Stratonovich transformations (HSTs) that are also suitable for spatially inhomogeneous trial functions. The discrete auxiliary fields introduced here are coupled to local spin or charge operators fluctuating around their Hartree-Fock values. The formalism can be considered a generalization of the discrete HSTs by J. E. Hirsch [Phys. Rev. B 28, 4059 (1983)] or a compactification of the shifted-contour auxiliary-field Monte Carlo formalism by N. Rom et al. [Chem. Phys. Lett. 270, 382 (1997)]. An improvement of the acceptance ratio is found for a real auxiliary field, while an improvement of the average sign is found for a purely imaginary auxiliary field. Efficiencies of the different HSTs are tested in the single-band Hubbard model at and away from half filling by studying the staggered magnetization and energy expectation values, respectively.Within the ground-state auxiliary-field quantum Monte Carlo technique, we introduce discrete Hubbard-Stratonovich transformations (HSTs) that are also suitable for spatially inhomogeneous trial functions. The discrete auxiliary fields introduced here are coupled to local spin or charge operators fluctuating around their Hartree-Fock values. The formalism can be considered a generalization of the discrete HSTs by J. E. Hirsch [Phys. Rev. B 28, 4059 (1983)] or a compactification of the shifted-contour auxiliary-field Monte Carlo formalism by N. Rom et al. [Chem. Phys. Lett. 270, 382 (1997)]. An improvement of the acceptance ratio is found for a real auxiliary field, while an improvement of the average sign is found for a purely imaginary auxiliary field. Efficiencies of the different HSTs are tested in the single-band Hubbard model at and away from half filling by studying the staggered magnetization and energy expectation values, respectively.

arXiv:1902.00321Physical review. B./Physical review. BApr 8, 201910 citations

Application of the path optimization method to a discrete spin system

Kouji Kashiwa, Yusuke Namekawa, Akira Ohnishi A +1 more

The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization method is applied by replacing the spins with dynamical variables, via the Hubbard-Stratonovich transformation, and the sum with the integral. The one-dimensional (Lenz-)Ising model with a complex coupling constant is used as a laboratory for the sign problem in the spin model. The average phase factor is enhanced by the path optimization method, indicating that the method can weaken the sign problem. Our result reproduces the analytic values with controlled statistical errors.The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization method is applied by replacing the spins with dynamical variables, via the Hubbard-Stratonovich transformation, and the sum with the integral. The one-dimensional (Lenz-)Ising model with a complex coupling constant is used as a laboratory for the sign problem in the spin model. The average phase factor is enhanced by the path optimization method, indicating that the method can weaken the sign problem. Our result reproduces the analytic values with controlled statistical errors.

arXiv:2309.06018Physical review. D/Physical review. D.Nov 13, 20232 citations

A numerical study of the sign problem in the Hubbard model using a modified discrete Hubbard-Stratonovich transformation

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A numerical study of the sign problem in the Hubbard model using a modified discrete Hubbard-Stratonovich transformation

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