Density dependent gauge field inducing emergent SSH physics, solitons and condensates in a discrete nonlinear Schr\"odinger equation

TL;DR

This paper explores how density-dependent gauge fields in a discrete nonlinear Schrödinger equation lead to emergent SSH physics, solitons, and condensates, revealing a rich phase transition and symmetry-protected edge modes.

Contribution

It introduces a novel model with density-dependent gauge fields causing phase transitions and emergent topological features in a discrete nonlinear Schrödinger system.

Findings

Ground-state transition from plane wave to soliton

Existence of stable condensate and soliton regimes

Emergent chiral symmetry with zero energy edge modes

Abstract

We investigate a discrete non-linear Schr\"odinger equation with dynamical, density-difference-dependent, gauge fields. We find a ground-state transition from a plane wave condensate to a localized soliton state as the gauge coupling is varied. Interestingly we find a regime in which the condensate and soliton are both stable. We identify an emergent chiral symmetry, which leads to the existence of a symmetry protected zero energy edge mode. The emergent chiral symmetry relates low and high energy solitons. These states indicate that the interaction acts both repulsively and attractively.