Chirally Protected State Manipulation by Tuning One-Dimensional Statistics

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 nontrivial Berry phases and holonomies in this chiral subspace. The corresponding states possess stationary checkerboard patterns in their N-particle densities that 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.