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Hamiltonian Monte Carlo enhanced by exact diagonalization

Finn L. Temmen1,*,†, Martina Gisti2,3,*,‡, David J. Luitz2,3, Thomas Luu1,4, and Johann Ostmeyer3,4

  • *These authors contributed equally to this work.
  • †Contact author: f.temmen@fz-juelich.de
  • ‡Contact author: mgisti@uni-bonn.de
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Phys. Rev. B 114, 185120 – Published 17 September, 2026

DOI: https://doi.org/10.1103/z8tf-fwfn

Abstract

Strongly correlated fermionic systems are of great interest in condensed matter physics and numerical methods are indispensable tools for their study. However, existing approaches such as exact diagonalization (ED) and stochastic quantum Monte Carlo methods each suffer from fundamental limitations: ED is hindered by exponential scaling in system size, while Monte Carlo methods are plagued by sign problems and long autocorrelation times. These limitations restrict the accessible parameter space and developing algorithms that efficiently alleviate them remains a central challenge in computational physics. In this work, we propose a hybrid algorithm that combines ED and Hamiltonian Monte Carlo (HMC) to simulate two-dimensional (2D) arrays of coupled quantum wires, modeled as interacting fermionic Hubbard chains. We demonstrate how our hybrid implementation of HMC, which we dub H2MC, outperforms either method alone across several key simulation facets. When compared to pure ED, H2MC has a much more favorable computational scaling, which allows us to push simulations to much larger 2D arrays. H2MC also greatly alleviates the sign problem and reduces autocorrelation times when compared to pure HMC formulations utilizing either real or imaginary auxiliary fields. Our formalism demonstrates how complementary strengths of seemingly disparate methods can be leveraged to enable feasible simulations in an extended parameter space.

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Phys. Rev. B 114, 185120– Published 17 September, 2026
  • Received 30 March 2026
  • Revised 11 August 2026
  • Accepted 13 August 2026
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