Strongly Coupled Lattice Gauge Theories and Antiferromagnetic Spin Systems

TL;DR

This thesis explores the strong coupling expansion of multiflavor lattice Schwinger models, mapping them onto antiferromagnetic spin chains to analyze chiral symmetry breaking and spectra, with results aligning with continuum weak coupling studies.

Contribution

It demonstrates a detailed mapping of lattice gauge theories onto quantum spin chains using strong coupling expansion, providing new insights into symmetry breaking and spectral properties.

Findings

Chiral symmetry breaking patterns identified

Spectral properties computed and compared with continuum results

Strong coupling results align qualitatively and quantitatively with weak coupling studies

Abstract

In this thesis, I use the strong coupling expansion to investigate the multiflavor lattice Schwinger models in the hamiltonian formalism using staggered fermions. In particular, I am interested in analysing the mapping of these gauge theories onto quantum spin-1/2 antiferromagnetic Heisenberg chains. Exploting this mapping, the chiral symmetry breaking patterns are studied and the spectra are computed. The extrapolation to zero lattice spacing of the results compare favorably qualitatively and quantitatively with the weak coupling studies of the gauge models in the continuum.