Homotopy data as part of the lattice field: A first study
Abstract
Fields exhibit a variety of topological properties, like different topological charges, when field space in the continuum is composed by more than one topological sector. Lattice treatments usually encounter difficulties describing those properties. In this work, we show that by augmenting the usual lattice fields to include extra variables describing local topological information (more precisely, regarding homotopy), the topology of the space of fields in the continuum is faithfully reproduced in the lattice. We apply this extended lattice formulation to some simple models with non-trivial topological charges, and we study their properties both analytically and via Monte Carlo simulations.
Cite
@article{arxiv.2105.14571,
title = {Homotopy data as part of the lattice field: A first study},
author = {Pietro Dall'Olio and José A. Zapata},
journal= {arXiv preprint arXiv:2105.14571},
year = {2023}
}
Comments
We added some references and a section where we make contact between the extended lattice formalism and the usual lattice variables augmented with an integer lattice field in the dual lattice. We made some corrections, including changing the title and the abstract, after referee's corrections and critiques