Reformulating Pfaffian Quantum Monte Carlo with the Hybrid Monte Carlo formalism
Abstract
Pfaffian quantum Monte Carlo extends auxiliary field methods to anomalous fermionic Hamiltonians, opening access to pairing systems and Hubbard--Stratonovich decompositions that are unavailable in determinant formulations. We show that this flexibility can be combined with the global updates of Hybrid Monte Carlo (HMC), leading to an algorithm scaling as 𝒪(NτL3), similar to its determinant quantum Monte Carlo (DQMC) counterpart without pseudofermions. The central observation is that the molecular dynamics force depends only on the magnitude of the Pfaffian weight, which admits a determinant representation and leads to a simplified force expression. This construction also yields unequal-time Majorana correlators at essentially no additional cost. We demonstrate the method for the interacting Kitaev chain using the imaginary and symmetric Majorana hopping channel. The resulting noncommuting auxiliary-field bond operators are treated through an even-odd decomposition. Their block structure permits an analytic reduction to a sparse effective interaction matrix of bandwidth two and allows explicit force expressions. Results agree with exact diagonalization and resolve low-energy modes localized at opposite boundaries, together with their increasing overlap near the topological transition of the non-interacting system. These findings establish HMC as an efficient sampling framework for Pfaffian auxiliary-field simulations.
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BibTeX
@misc{hauschild2026reformulating,
title = {{Reformulating Pfaffian Quantum Monte Carlo with the Hybrid Monte Carlo formalism}},
author = {Thomas Hauschild and Lin Wang and Finn L. Temmen and Thomas Luu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.21631},
eprint = {2609.21631},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21631},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reformulating Pfaffian Quantum Monte Carlo with the Hybrid Monte Carlo formalism
AU - Thomas Hauschild
AU - Lin Wang
AU - Finn L. Temmen
AU - Thomas Luu
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2609.21631
UR - https://arxiv.org/abs/2609.21631
AB - Pfaffian quantum Monte Carlo extends auxiliary field methods to anomalous fermionic Hamiltonians, opening access to pairing systems and Hubbard--Stratonovich decompositions that are unavailable in determinant formulations. We show that this flexibility can be combined with the global updates of Hybrid Monte Carlo (HMC), leading to an algorithm scaling as 𝒪(N_τL^3), similar to its determinant quantum Monte Carlo (DQMC) counterpart without pseudofermions. The central observation is that the molecular dynamics force depends only on the magnitude of the Pfaffian weight, which admits a determinant representation and leads to a simplified force expression. This construction also yields unequal-time Majorana correlators at essentially no additional cost. We demonstrate the method for the interacting Kitaev chain using the imaginary and symmetric Majorana hopping channel. The resulting noncommuting auxiliary-field bond operators are treated through an even-odd decomposition. Their block structure permits an analytic reduction to a sparse effective interaction matrix of bandwidth two and allows explicit force expressions. Results agree with exact diagonalization and resolve low-energy modes localized at opposite boundaries, together with their increasing overlap near the topological transition of the non-interacting system. These findings establish HMC as an efficient sampling framework for Pfaffian auxiliary-field simulations.
ER -