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Algorithmic aspects of gauged Gaussian fermionic projected entangled pair states: Gauge fixing and translation invariance

Itay Gomelski1, Jonathan Elyovich1, Ariel Kelman2, Erez Zohar1, and Patrick Emonts3,4,5,6

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Phys. Rev. Research 8, 023240 – Published 2 June, 2026

DOI: https://doi.org/10.1103/xjvk-hks4

Abstract

Lattice gauge theories (LGTs) provide a powerful framework for studying nonperturbative phenomena in gauge theories. However, conventional approaches such as Monte Carlo (MC) simulations in imaginary time are limited, as they do not allow real-time evolution and suffer from a sign problem in many important cases. Using gauged Gaussian fermionic projected entangled pair states (GGFPEPS) as a variational ground-state ansatz offers an alternative for studying LGTs through a sign-problem-free variational MC. As this method is extended to larger and more complex systems, understanding its numerical behavior becomes essential. While conventional action-based MC has been extensively studied, the performance and characteristics of non-action-based MC within the GGFPEPS framework are far less explored. In this work, we investigate these algorithmic aspects, identifying an optimal update size for GGFPEPS-based MC simulations for Z2 in 2+1 dimensions. We show that gauge fixing generally slows convergence and demonstrate that not exploiting the translation invariance can, in some cases, improve the computational time scaling of error convergence. We expect that these improvements will allow advancing the simulation to larger and more complex systems.

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Phys. Rev. Research 8, 023240– Published 2 June, 2026
  • Received 14 January 2026
  • Accepted 17 April 2026
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