The transition of 2-dimensional solitons to 1-dimensional ones on hexagonal lattices

TL;DR

This paper investigates how two-dimensional solitons in a hexagonal lattice system transition into one-dimensional solitons as the electron-phonon coupling constant decreases, revealing a dimensional crossover near a critical coupling value.

Contribution

It demonstrates the transition of 2D solitons to 1D solitons in a hexagonal lattice system as the coupling constant approaches a critical threshold, extending previous work on soliton existence.

Findings

2D solitons become broad and effectively 1D near critical coupling

Soliton existence depends on sufficiently large electron-phonon coupling

Dimensional crossover occurs close to the critical coupling value

Abstract

We study solitons arising in a system describing the interaction of a two-dimensional discrete hexagonal lattice with an additional electron field (or, in general, an exciton field). We assume that this interaction is electron-phonon-like. In our previous paper [4], we have studied the existence of two-dimensional solitons and have found that these solitons exist only if the electron-phonon coupling constant is sufficiently large. In this paper, we report the results of our investigation for small values of this constant, close to its critical value for the existence of solitons. We find that as the coupling decreases the soliton gets very broad and then becomes effectively one-dimensional.