Sign-problem-free Bosonic Auxiliary Field Quantum Monte Carlo
Abstract
The sign problem poses a fundamental barrier to numerically exact quantum Monte Carlo simulations, severely hindering our understanding of quantum many-body physics across disciplines ranging from condensed matter to particle and nuclear physics. Geometrical frustration makes this barrier especially acute for interacting bosons. Here, we develop a bosonic auxiliary-field quantum Monte Carlo (BAFQMC) method and rigorously prove that time-reversal symmetry and reflection positivity each provide a general sufficient condition for sign-problem-free simulations. Crucially, under either criterion, BAFQMC evades the sign problem even on frustrated lattices where conventional world-line and stochastic-series-expansion methods fail. Benchmarking our approach on a two-flavor Bose-Hubbard model on the triangular lattice yields excellent quantitative agreement with finite-temperature exact diagonalization. By establishing unifying principles to solve the sign problem in BAFQMC, our work substantially expands the reach of unbiased, numerically exact simulations for frustrated bosonic matter.
Related
- Bosonic SPT and invertible phases and its relation to Steenrod's problem
- Integrable auxiliary field sigma model and the metric approach to TT̅-like deformations
- Dynamical classical-field limit of Bosonic Gibbs states: Renormalized Hartree NLS correlations in 2D and 3D
- Quantum cluster structures on bosonic extensions
- Improved lower bound for the two-way-assisted quantum capacity of the bosonic thermal-loss channel
BibTeX
@misc{yu2026signproblemfree,
title = {{Sign-problem-free Bosonic Auxiliary Field Quantum Monte Carlo}},
author = {Yin-Kai Yu and Zhong-Chao Wei and Zi-Xiang Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31541},
eprint = {2610.31541},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31541},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sign-problem-free Bosonic Auxiliary Field Quantum Monte Carlo
AU - Yin-Kai Yu
AU - Zhong-Chao Wei
AU - Zi-Xiang Li
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31541
UR - https://arxiv.org/abs/2610.31541
AB - The sign problem poses a fundamental barrier to numerically exact quantum Monte Carlo simulations, severely hindering our understanding of quantum many-body physics across disciplines ranging from condensed matter to particle and nuclear physics. Geometrical frustration makes this barrier especially acute for interacting bosons. Here, we develop a bosonic auxiliary-field quantum Monte Carlo (BAFQMC) method and rigorously prove that time-reversal symmetry and reflection positivity each provide a general sufficient condition for sign-problem-free simulations. Crucially, under either criterion, BAFQMC evades the sign problem even on frustrated lattices where conventional world-line and stochastic-series-expansion methods fail. Benchmarking our approach on a two-flavor Bose-Hubbard model on the triangular lattice yields excellent quantitative agreement with finite-temperature exact diagonalization. By establishing unifying principles to solve the sign problem in BAFQMC, our work substantially expands the reach of unbiased, numerically exact simulations for frustrated bosonic matter.
ER -