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arXiv · 2211.05074

A flexible class of exact Hubbard-Stratonovich transformations

Seher Karakuzu·Benjamin Cohen-Stead·Cristian D. Batista·Steven Johnston·Kipton Barros
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Abstract

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 ($p=\infty$) to a compact auxiliary field that couples to electrons sinusoidally ($p=0$). In tests on the single-band Hubbard model, we find that the severity of the sign problem decreases systematically with increasing $p$. Selecting $p$ finite, however, enables continuous sampling methods like the Langevin or Hamiltonian Monte Carlo methods. We explore the tradeoffs between various simulation methods through numerical benchmarks.

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Seher Karakuzu, Benjamin Cohen-Stead, Cristian D. Batista, Steven Johnston, Kipton Barros. 2022-11-09. A flexible class of exact Hubbard-Stratonovich transformations. https://doi.org/10.1103/physreve.107.055301

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