Quantum cluster approach to the topological invariants in correlated Chern insulators

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.

References in corpus (27)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Interacting topological insulators: a review
• Variational cluster approach to correlated electron systems in low dimensions
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
• Simplified topological invariants for interacting insulators
• Correlation effects in two-dimensional topological insulators
• Mott Physics and Topological Phase Transition in Correlated Dirac Fermions
• The Hubbard model on the triangular lattice: Spiral order and spin liquid
• First order character and observable signatures of topological quantum phase transitions
• Topological phase transitions in the repulsively interacting Haldane-Hubbard model
• First order Mott transition at zero temperature in two dimensions: Variational plaquette study
• Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined Quantum Monte Carlo and Green's function study
• First order topological phase transition of the Haldane--Hubbard model
• Spectral properties of the square-lattice antiferromagnetic J1-J2 Heisenberg model: confinement and deconfinement of spinons
• Quantum cluster approach to the spinful Haldane-Hubbard model
• Variational cluster approach for strongly correlated lattice bosons in the superfluid phase
• Mean field study of the topological Haldane-Hubbard model of spin-$1/2$ fermions
• Topological invariants for the Haldane phase of interacting SSH chains -- a functional RG approach
• Topological phase transitions and universality in the Haldane-Hubbard model
• Quantum paramagnet in a $\pi$ flux triangular lattice Hubbard model
• Topological invariants in interacting Quantum Spin Hall: a Cluster Perturbation Theory approach
• Parity-mixing superconducting phase in the Rashba-Hubbard model and its topological properties from dynamical mean field theory
• Phase diagram and topological phases in the triangular lattice Kitaev-Hubbard model
• Topological order in the Haldane model with spin-spin on-site interactions

Cited by in corpus (5)

• Topological Mott transition in a Weyl-Hubbard model with dynamical mean-field theory
• Antiferromagnetic Chern insulator with large charge gap in heavy transition-metal compounds
• Antiferromagnetic topological insulators in heavy-fermion systems
• From explicit to spontaneous charge order and the fate of antiferromagnetic quantum Hall state
• Pseudogap with Fermi arcs and Fermi pockets in half-filled twisted transition metal dichalcogenides