Numerical investigations of the Schwinger model and selected quantum spin models

TL;DR

This paper conducts numerical investigations of the Schwinger model and quantum spin models using various computational methods, providing results consistent with theoretical predictions and highlighting the effectiveness of DMRG.

Contribution

It applies multiple numerical techniques to study the Schwinger and quantum spin models, offering new insights and confirming previous theoretical results.

Findings

DMRG results are highly promising

Energy levels match exact values

Model parameters align with theoretical predictions

Abstract

Numerical investigations of the XY model, the Heisenberg model and the J-J' Heisenberg model are conducted, using the exact diagonalisation, the numerical renormalisation and the density matrix renormalisation group approach. The low-lying energy levels are obtained and finite size scaling is performed to estimate the bulk limit values. The results are found to be consistent with the exact values. The DMRG results are found to be most promising. The Schwinger model is also studied using the exact diagonalisation and the strong coupling expansion. The massless, the massive model and the model with a background electric field are explored. Ground state energy, scalar and vector particle masses and order parameters are examined. The achieved values are observed to be consistent with previous results and theoretical predictions. Path to the future studies is outlined.