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Tensor network simulations of quasi-GPDs in the massive Schwinger model

Sebastian Grieninger1,2,3,4,*, Jake Montgomery4,†, Felix Ringer4,‡, and Ismail Zahed4,§

  • *Contact author: segrie@uw.edu
  • †Contact author: jake.montgomery@stonybrook.edu
  • ‡Contact author: felix.ringer@stonybrook.edu
  • §Contact author: ismail.zahed@stonybrook.edu
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Phys. Rev. D 113, 074509 – Published 14 April, 2026

DOI: https://doi.org/10.1103/sz3z-8cyx

Abstract

Generalized parton distribution functions (GPDs) are off-diagonal light-cone matrix elements that encode the internal structure of hadrons in terms of quark and gluon degrees of freedom. In this work, we present the first nonperturbative study of quasi-GPDs in the massive Schwinger model, quantum electrodynamics in 1+1 dimensions (QED2), within the Hamiltonian formulation of lattice field theory. Quasidistributions are spatial correlation functions of boosted states, which approach the relevant light-cone distributions in the luminal limit. Using tensor networks, we prepare the first excited state in the strongly coupled regime and boost it to close to the light-cone on lattices of up to 400 lattice sites. We compute both quasiparton distribution functions and, for the first time, quasi-GPDs, and study their convergence for increasingly boosted states. In addition, we perform analytic calculations of GPDs in the two-particle Fock-space approximation and in the Reggeized limit, providing qualitative benchmarks for the tensor network results. Our analysis establishes computational benchmarks for accessing partonic observables in low-dimensional gauge theories, offering a starting point for future extensions to higher dimensions, non-Abelian theories, and quantum simulations.

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Phys. Rev. D 113, 074509– Published 14 April, 2026
  • Received 9 December 2025
  • Accepted 17 March 2026
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