Direct computation of Parton Distribution Functions with Tensor Networks

Mari Carmen Bañuls^1,2, Krzysztof Cichy³, C.-J. David Lin^4,5, Manuel Schneider^4*

¹Max-Planck-Institut für Quantenoptik, Garching, Germany
²Munich Center for Quantum Science and Technology (MCQST), Munich, Germany
³Faculty of Physics and Astronomy, Adam Mickiewicz University, Poznań, Poland
⁴Institute of Physics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan
⁵Centre for High Energy Physics, Chung-Yuan Christian University, Taoyuan, Taiwan

* Presenter:Manuel Schneider, email:manuel.schneider@nycu.edu.tw

Parton distribution functions (PDFs) describe universal properties of bound states and allow us to calculate scattering amplitudes in processes with large momentum transfer. Calculating PDFs involves the evaluation of matrix elements with a Wilson line in a light-cone direction. While these matrix elements can only be indirectly be accessed by Monte Carlo methods in Euclidean spacetime, a direct evaluation is possible in Minkowski-space using the Hamiltonian formalism. The necessary spatial- and time-evolution can be efficiently applied using tensor network states. We demonstrate the method by calculating the PDF of the vector meson in the Schwinger model with matrix product states.

Keywords: Parton Distribution Functions, Schwinger Model, Tensor Networks, Matrix Product States, Real-time evolution