arXiv subjects

Jonathan Elyovich

Publications and source records attributed to Jonathan Elyovich.

3 recordsLinked to original sources

arXiv2026

ggpeps: A package for Gauged Gaussian PEPS

Lattice gauge theories are a low-energy regularization of quantum field theories. They are the basis for the development of numerical algorithms that provide insight into the non-perturbative regime of quantum field theories which is difficult to achieve through other methods. We present a python package, ggpeps, implementing gauged Gaussian projected entangled pair states (GGPEPS), specialized to study lattice gauge theories. We give a an overview of the considered systems, describe the GGPEPS ansatz and provide a usage guide for the ggpeps package.

hep-lat↗

arXiv2025

Algorithmic Aspects of Gauged Gaussian Fermionic PEPS: Gauge Fixing and Translation Invariance

Lattice gauge theories (LGTs) provide a powerful framework for studying non-perturbative 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 $\mathbb{Z}_2$ 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.

hep-lat↗

arXiv2024

Gauged Gaussian PEPS -- A High Dimensional Tensor Network Formulation for Lattice Gauge Theories

Gauge theories form the basis of our understanding of modern physics - ranging from the description of quarks and gluons to effective models in condensed matter physics. In the non-perturbative regime, gauge theories are conventionally treated discretely as lattice gauge theories. The resulting systems are evaluated with path-integral based Monte Carlo methods. These methods, however, can suffer from the sign problem and do not allow for a direct evaluation of real-time dynamics. In this work, we present a unified and comprehensive framework for gauged Gaussian Projected Entangled Pair States (PEPS), a variational ansatz based on tensor networks. We review the construction of Hamiltonian lattice gauge theories, explain their similarities with PEPS, and detail the construction of the state. The estimation of ground states is based on a variational Monte Carlo procedure with the PEPS as an ansatz state. This sign-problem-free ansatz can be efficiently evaluated in any dimension with arbitrary gauge groups, and can include dynamical fermionic matter, suggesting new options for the simulation of non-perturbative regimes of gauge theories, including QCD.

hep-lat↗