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

TL;DR

This paper uses tensor network methods to nonperturbatively compute quasi-GPDs in the massive Schwinger model, demonstrating the approach's potential for studying hadronic structure in low-dimensional gauge theories.

Contribution

It presents the first nonperturbative calculation of quasi-GPDs in the massive Schwinger model using tensor networks, including boosted states and analytic benchmarks.

Findings

Successfully computed quasi-GPDs in the strongly coupled regime.

Demonstrated convergence of quasi-GPDs with increasing boost.

Provided analytic benchmarks for tensor network results.

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. Quasi-distributions 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 quasi-parton 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.