Topological invariant and cotranslational symmetry in strongly interacting multi-magnon systems

TL;DR

This paper introduces a new method to characterize topological states in strongly interacting multi-particle quantum systems using a generalized Chern invariant derived from cotranslational symmetry, demonstrated on a multi-magnon Heisenberg XXZ model.

Contribution

It develops a systematic approach to define a topological invariant for interacting states, extending the concept of the Thouless-Kohmoto-Nightingale-den Nijs invariant to multi-particle systems.

Findings

Identification of topological edge bound-states in a multi-magnon system.

Construction of a topological phase diagram for the model.

Derivation of an effective Hofstadter superlattice model.

Abstract

It is still an outstanding challenge to characterize and understand the topological features of strongly interacting states such as bound-states in interacting quantum systems. Here, by introducing a cotranslational symmetry in an interacting multi-particle quantum system, we systematically develop a method to define a Chern invariant, which is a generalization of the well-known Thouless-Kohmoto-Nightingale-den Nijs invariant, for identifying strongly interacting topological states. As an example, we study the topological multi-magnon states in a generalized Heisenberg XXZ model, which can be realized by the currently available experiment techniques of cold atoms [Phys. Rev. Lett. \textbf{111}, 185301 (2013); Phys. Rev. Lett. \textbf{111}, 185302 (2013)]. Through calculating the two-magnon excitation spectrum and the defined Chern number, we explore the emergence of topological edge bound-states and give their topological phase diagram. We also analytically derive an effective single-particle Hofstadter superlattice model for a better understanding of the topological bound-states. Our results not only provide a new approach to defining a topological invariant for interacting multi-particle systems, but also give insights into the characterization and understanding of strongly interacting topological states.