Phase-diagram and quasiparticles of a lattice SU(2) scalar-fermion model in (2+1) dimensions

TL;DR

This study explores the phase diagram and quasiparticle excitations of a lattice SU(2) scalar-fermion model in (2+1) dimensions, focusing on strong coupling regimes using numerical and Mean-Field methods.

Contribution

It introduces a new adaptation of the Hybrid Monte Carlo algorithm for the O(3) non-linear sigma model and analyzes charged excitations and bound states in different phases.

Findings

Bound states of two charged fermions in the paramagnetic phase

Emergence of fermionic excitations around specific momenta in the antiferromagnetic phase

Development of a new Monte Carlo method for the O(3) model

Abstract

The phase diagram at zero temperature of a lattice SU(2) scalar-fermion model in (2+1) dimensions is studied numerically and with Mean-Field methods. Special attention is devoted to the strong coupling regime. We have developed a new method to adaptate the Hybrid Monte Carlo algorithm to the O(3) non-linear $\sigma$ model constraint. The charged excitations in the various phases are studied at the Mean-Field lev el. Bound states of two charged fermions are found in a strongly coupled {\it paramagnetic} phase. On the other hand, in the strongly coupled antiferromagnetic phase fermionic excitations around momenta $(\pm\frac{\pi}{2},\pm\frac{\pi}{2},\pm\frac{\pi}{2})$ emerge.