Interplay of local order and topology in the extended Haldane-Hubbard model

TL;DR

This study explores the complex phase diagram of the extended Haldane-Hubbard model on a honeycomb lattice, revealing the interplay between local order parameters and topological properties using multiple computational methods.

Contribution

It provides a comprehensive analysis combining exact diagonalization, mean-field, and DMRG to clarify the relationship between local order and topology in the model.

Findings

Local order parameters can coexist with nontrivial topology in finite systems.

Topologically nontrivial insulators are characterized by a nonlocal order.

Finite-size effects can mislead conclusions about the coexistence of order and topology.

Abstract

We investigate the ground-state phase diagram of the spinful extended Haldane-Hubbard model on the honeycomb lattice using an exact-diagonalization, mean-field variational approach, and further complement it with the infinite density matrix renormalization group, applied to an infinite honeycomb cylinder. This model, governed by both on-site and nearest-neighbor interactions, can result in two types of insulators with finite local order parameters, either with spin or charge ordering. Moreover, a third one, a topologically nontrivial insulator with nonlocal order, is also manifest. We test expectations of previous analyses in spinless versions asserting that once a local order parameter is formed, the topological characteristics of the ground state, associated with a finite Chern number, are no longer present, resulting in a topologically trivial wave function. Our study confirms this overall picture, and highlights how finite-size effects may result in misleading conclusions on the coexistence of finite local order parameters and nontrivial topology in this model.