Physical realization and possible identification of topological excitations in quantum Heisenberg anti-ferromagnet on a two dimensional lattice

TL;DR

This paper investigates topological excitations in a 2D quantum Heisenberg antiferromagnet, emphasizing the role of a Wess-Zumino-like term in identifying vortices and anti-vortices with odd topological charges.

Contribution

It introduces a novel formalism using a WZ-like term to distinguish quantum vortices and anti-vortices in a 2D quantum antiferromagnet, differing from conventional methods.

Findings

WZ-like term distinguishes vortices and anti-vortices with odd topological charges

Constructs quantum vortices using coherent staggered spin fields

Highlights the role of the WZ-like term in topological excitation identification

Abstract

Physical spin configurations corresponding to topological excitations, expected to be present in the XY limit of a quantum spin 1/2 Heisenberg anti-ferromagnet, are probed on a two dimensional square lattice . Quantum vortices (anti-vortices) are constructed in terms of coherent staggered spin field components, as limiting case of meronic (anti-meronic) configurations . The crucial role of the associated Wess-Zumino-like (WZ-like) term is highlighted in our procedure . The time evolution equation of coherent spin fields used in this analysis is obtained by applying variational principle on the quantum Euclidean action corresponding to the Heisenberg anti-ferromagnet on lattice . It is shown that the WZ-like term can distinguish between vortices and anti-vortices only in a charge sector with odd topological charges. Our formalism is distinctly different from the conventional approach for the construction of quantum vortices (anti-vortices) .