# Dynamically Induced Topology and Quantum Monodromies in a Proximity Quenched Gapless Wire

## TL;DR

This paper demonstrates how coupling a trivial gapless wire to topological bound states induces measurable topological properties and quantum monodromies dynamically, even in the presence of disorder and interactions.

## Contribution

It introduces a novel mechanism for dynamically inducing topological features in a gapless wire through quench dynamics with topological bound states.

## Key findings

- Topological signatures persist over long times after quench.
- Dynamically induced topology characterized by fractional charge and fermion parity.
- Topological monodromies generated by boundary correlators in the wire.

## Abstract

We study the quench dynamics of a topologically trivial one-dimensional gapless wire following its sudden coupling to topological bound states. We find that as the bound states leak into and propagate through the wire, signatures of their topological nature survive and remain measurable over a long lifetime. Thus, the quench dynamically induces topological properties in the gapless wire. Specifically, we study a gapless wire coupled to fractionally charged solitons or Majorana fermions and characterize the dynamically induced topology in the wire, in the presence of disorder and short-range interactions, by analytical and numerical calculations of the dynamics of fractional charge, fermion parity, entanglement entropy, and fractional exchange statistics. In a dual effective description, this phenomenon is described by correlators of boundary changing operators, which, remarkably, generate topologically non-trivial monodromies in the gapless wire, both for abelian and non-abelian quantum statistics of the bound states.