Mapping Chern numbers in quasi-periodic interacting spin chains

TL;DR

This paper explores topological phases in quasi-periodic interacting spin chains, demonstrating the generation and stability of Chern numbers at finite magnetization densities through numerical simulations and algebraic reformulation.

Contribution

It introduces a method to realize and analyze topological phases with Chern numbers in finite-density spin chains, linking algebraic approaches with numerical validation.

Findings

Chern numbers can be generated at finite magnetization densities.

The stability and quantization of Chern numbers are confirmed numerically.

Edge spectrum relations are discussed in the context of bulk-boundary correspondence.

Abstract

Quasi-periodic quantum spin chains were recently found to support many topological phases in the finite magnetization sectors. They can simulate strong topological phases from class A in arbitrary dimension that are characterized by first and higher order Chern numbers. In the present work, we use those findings to generate topological phases at finite magnetization densities that carry first Chern numbers. Given the reduced dimensionality of the spin chains, this provides a unique opportunity to investigate the bulk-boundary correspondence as well as the stability and quantization of the Chern number in the presence of interactions. The later is reformulated using a torus action on the algebra of observables and its quantization and stability is confirmed by numerical simulations. The relations between Chern values and the observed edge spectrum are also discussed.