Sign-Resolved Statistics and the Origin of Bias in Quantum Monte Carlo
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918230437658624 |
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| author | Larson, Ryan Mondaini, Rubem Scalettar, Richard T. |
| author_facet | Larson, Ryan Mondaini, Rubem Scalettar, Richard T. |
| contents | Quantum simulations are a powerful tool for exploring strongly correlated many-body phenomena. Yet, their reach is limited by the fermion sign problem, which causes configuration weights to become negative, compromising statistical sampling. In auxiliary-field Quantum Monte Carlo calculations of the doped Hubbard model, neglecting the sign ${\cal S}$ of the weight leads to qualitatively wrong results -- most notably, an apparent suppression rather than enhancement of $d$-wave pairing at low temperature. Here we approach the problem from a different perspective: instead of identifying negative-weight paths, we examine the statistics of measured observables in a sign-resolved manner. By analyzing histograms of key quantities (kinetic energy, antiferromagnetic structure factor, and pair susceptibilities) for configurations with ${\cal S}=\pm1$, we derive an exact relation linking the bias from ignoring the sign to the difference between sign-resolved means, $Δμ$, and the average sign, $\langle {\cal S}\rangle$. Our framework provides a precise diagnostic of the origin of measurement bias in Quantum Monte Carlo and clarifies why observables such as the $d$-wave susceptibility are especially sensitive to the sign problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04056 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sign-Resolved Statistics and the Origin of Bias in Quantum Monte Carlo Larson, Ryan Mondaini, Rubem Scalettar, Richard T. Strongly Correlated Electrons Quantum simulations are a powerful tool for exploring strongly correlated many-body phenomena. Yet, their reach is limited by the fermion sign problem, which causes configuration weights to become negative, compromising statistical sampling. In auxiliary-field Quantum Monte Carlo calculations of the doped Hubbard model, neglecting the sign ${\cal S}$ of the weight leads to qualitatively wrong results -- most notably, an apparent suppression rather than enhancement of $d$-wave pairing at low temperature. Here we approach the problem from a different perspective: instead of identifying negative-weight paths, we examine the statistics of measured observables in a sign-resolved manner. By analyzing histograms of key quantities (kinetic energy, antiferromagnetic structure factor, and pair susceptibilities) for configurations with ${\cal S}=\pm1$, we derive an exact relation linking the bias from ignoring the sign to the difference between sign-resolved means, $Δμ$, and the average sign, $\langle {\cal S}\rangle$. Our framework provides a precise diagnostic of the origin of measurement bias in Quantum Monte Carlo and clarifies why observables such as the $d$-wave susceptibility are especially sensitive to the sign problem. |
| title | Sign-Resolved Statistics and the Origin of Bias in Quantum Monte Carlo |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2512.04056 |