Chirally-protected state manipulation by tuning one-dimensional statistics

TL;DR

This paper demonstrates how tuning the statistical parameter in an anyon-Hubbard model can protect zero-energy states through chiral symmetry, enabling adiabatic control and observation of non-trivial Berry phases in lattice systems.

Contribution

It introduces a method to manipulate chiral symmetry-protected states via statistical parameter tuning, providing explicit protocols for their preparation, observation, and control.

Findings

Chiral symmetry protects a degenerate zero-energy subspace.

Adiabatic evolution yields non-trivial Berry phases and holonomies.

Stationary checkerboard density patterns are preserved during manipulation.

Abstract

Chiral symmetry is broken by typical interactions in lattice models, but the statistical interactions embodied in the anyon-Hubbard model are an exception. This is an example for a correlated hopping model where chiral symmetry protects a degenerate zero-energy subspace. Complementary to the traditional approach of anyon braiding in real space, we adiabatically evolve the statistical parameter and find non-trivial Berry phases and holonomies in this chiral subspace. The corresponding states possess stationary checkerboard patterns in their $N$-particle densities which are preserved under adiabatic manipulation. We give an explicit protocol for how these chirally-protected zero-energy states can be prepared, observed, validated, and controlled.