Implementing a Lattice Formulation of the Schwinger Modelwith Periodic Boundary Conditions Using Tensor Networks

I attempt to develop a simple tensor network formulation of the Schwinger model with periodic boundary conditions. The primary challenge is to enforce the local constraints imposed by Gauss's Law. I do this by combining global conservation of a specially defined quantum number with the local optimization steps used in the density matrix renormalization group (DMRG) algorithm for finding the ground state of a quantum system. However, due to practical constraints, I still use matrix product states and matrix product operators with open boundary conditions. I demonstrate the efficacy of the model in computing the bulk limit (the limit as the number of lattice sites goes to infinity) for the energy density, chiral condensate, and electric field energy density of the ground state. Future investigation should begin with recreating the model using periodic matrix product states and matrix product operators and using a version of DMRG that has been optimized for periodic boundary conditions.

Name thesis:degree_name

Bachelor

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Physics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2021

Author dc:creator

• Kazi, Sujay

Advisor dc:contributor.advisor

• Shanahan, Phiala

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright retained by author(s)

Licence dc:rights.uri

• https://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/139158

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/139158