Relationship between two-particle topology and fractional Chern insulator

TL;DR

This study explores how the topological properties of two-particle systems relate to the emergence of fractional Chern insulator states in many-body lattice models, providing a new perspective on FCI search principles.

Contribution

It introduces a two-particle Chern number framework and demonstrates its correlation with FCI ground states across various models, advancing understanding of FCI formation criteria.

Findings

Two-particle Chern number correlates with FCI presence in most models.

Nontrivial two-particle topology indicates similarity to FQH systems.

Two-band models show exceptions to the correlation.

Abstract

Lattice generalizations of fractional quantum Hall (FQH) systems, called fractional Chern insulators (FCIs), have been extensively investigated in strongly correlated systems. Despite many efforts, previous studies have not revealed all of the guiding principles for the FCI search. In this paper, we investigate a relationship between the topological band structure in the two-particle problem and the FCI ground states in the many-body problem. We first formulate the two-particle problem of a bosonic on-site interaction projected onto the lowest band of a given tight-binding Hamiltonian. We introduce a reduced Hamiltonian whose eigenvalues correspond to the two-particle bound-state energies. By using the reduced Hamiltonian, we define the two-particle Chern number and numerically check the bulk-boundary correspondence that is predicted by the two-particle Chern number. We then propose that a nontrivial two-particle Chern number of dominant bands roughly indicates the presence of bosonic FCI ground states at filling factor $\nu=1/2$. We numerically investigate this relationship in several tight-binding models with Chern bands and find that it holds well in most of the cases, albeit two-band models being exceptions. Although the two-particle topology is neither a necessary nor a sufficient condition for the FCI state as other indicators in previous studies, our numerical results indicate that the two-particle topology characterizes the degree of similarity to the FQH systems.