Quantum cluster approach to the topological invariants in correlated Chern insulators

TL;DR

This paper introduces a quantum cluster approach to accurately compute topological invariants in strongly correlated Chern insulators, addressing limitations of previous methods by considering enlarged unit cells to preserve translation symmetry.

Contribution

It demonstrates that the interacting bulk Chern number can be correctly calculated using an enlarged unit cell in quantum cluster methods, overcoming symmetry-breaking issues.

Findings

Standard schemes fail due to translation symmetry breaking.

Enlarged unit cell approach restores correct topological invariant calculation.

Method aligns with bulk-edge correspondence in correlated systems.

Abstract

We detect the topological properties of Chern insulators with strong Coulomb interactions by use of cluster perturbation theory and variational cluster approach. The common scheme in previous studies only involves the calculation of the interacting bulk Chern number within the natural unit cell by means of the so-called topological Hamiltonian. With close investigations on a prototype model, the half-filled Haldane Hubbard model, which is subject to both periodic and open boundary conditions, we uncover the unexpected failure of this scheme due to the explicit breaking of the translation symmetry. Instead, we assert that the faithful interacting bulk Chern number in the framework of quantum cluster approaches can be computed in the enlarged unit cell, which is free of the fault caused by the explicit translation symmetry breaking and consistent with the interacting bulk-edge correspondence.