# $\mathbb{Z}_n$ solitons in intertwined topological phases

## TL;DR

This paper investigates dynamical topological defects in a strongly-correlated one-dimensional $ ext{Z}_2$ Bose-Hubbard model, revealing fractionalized quasi-particles, soliton lattices, and a generalized bulk-defect correspondence with potential experimental realizations.

## Contribution

It introduces a novel analysis of dynamical $ ext{Z}_n$ solitons in intertwined topological phases, extending understanding beyond static defect approximations and establishing a topological pumping mechanism.

## Key findings

- Fractionalized bosonic quasi-particles bound to solitons.
- Formation of a fractional soliton lattice at high densities.
- Quantized inter-soliton transport demonstrating a bulk-defect correspondence.

## Abstract

Topological phases of matter can support fractionalized quasi-particles localized at topological defects. The current understanding of these exotic excitations, based on the celebrated bulk-defect correspondence, typically relies on crude approximations where such defects are replaced by a static classical background coupled to the matter sector. In this work, we explore the strongly-correlated nature of symmetry-protected topological defects by focusing on situations where such defects arise spontaneously as dynamical solitons in intertwined topological phases, where symmetry breaking coexists with topological symmetry protection. In particular, we focus on the $\mathbb{Z}_2$ Bose-Hubbard model, a one-dimensional chain of interacting bosons coupled to $\mathbb{Z}_2$ fields, and show how solitons with $\mathbb{Z}_n$ topological charges appear for particle/hole dopings about certain commensurate fillings, extending the results of [1] beyond half filling. We show that these defects host fractionalized bosonic quasi-particles, forming bound states that travel through the system unless externally pinned, and repel each other giving rise to a fractional soliton lattice for sufficiently high densities. Moreover, we uncover the topological origin of these fractional bound excitations through a pumping mechanism, where the quantization of the inter-soliton transport allows us to establish a generalized bulk-defect correspondence. This in-depth analysis of dynamical topological defects bound to fractionalized quasi-particles, together with the possibility of implementing our model in cold-atomic experiments, paves the way for further exploration of exotic topological phenomena in strongly-correlated systems.