Topological invariants for interacting topological insulators: I. Efficient numerical evaluation scheme and implementations

Abstract

The aim of this series of two papers is to discuss topological invariants for interacting topological insulators (TIs). In the first paper (I), we provide a paradigm of efficient numerical evaluation scheme for topological invariants, in which we demystify the procedures and techniques employed in calculating Z2 invariant and spin Chern number via zero-frequency single-particle Green's function in quantum Monte Carlo (QMC) simulations. Here we introduce a periodization process to overcome the ubiquitous finite-size effect, so that the calculated spin Chern number shows ideally quantized values. We also show that making use of symmetry properties of the underlying systems can greatly reduce the computational effort. To demonstrate the effectiveness of our numerical evaluation scheme, especially the periodization process, of topological invariants, we apply it on two independent two-dimensional models of interacting topological insulators. In the subsequent paper (II), we apply the scheme developed here to wider classes of models of interacting topological insulators, for which certain limitation of constructing topological invariant via single-particle Green's functions will be presented.

20 pages, 8 figures

References in corpus (14)

• Topological Insulators with Inversion Symmetry
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Robustness of the Spin-Chern number
• Correlated Topological Insulators with Mixed Valence
• Simplified topological invariants for interacting insulators
• Topological field theory and thermal responses of interacting topological superconductors
• First order character and observable signatures of topological quantum phase transitions
• Characterization of a topological Mott insulator in one dimension
• Strongly Correlated Topological Superconductors and Topological Phase Transitions via Green's Function
• Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined Quantum Monte Carlo and Green's function study
• Cellular dynamical mean-field theory study of an interacting topological honeycomb lattice model at finite temperature
• Topological invariants in interacting Quantum Spin Hall: a Cluster Perturbation Theory approach
• Topological properties of the bond-modulated honeycomb lattice

Cited by in corpus (19)

• Duality between the deconfined quantum-critical point and the bosonic topological transition
• In-plane Zeeman field induced Majorana corner and hinge modes in an $s$-wave superconductor heterostructure
• Strong Correlation Effects on Topological Quantum Phase Transitions in Three Dimensions
• Dynamical Generation of Topological Masses in Dirac Fermions
• The interacting Rice-Mele model: bulk and boundaries
• Topological invariants for interacting topological insulators: II. Breakdown of the Green's function formalism
• Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking
• Antiferromagnetic spin valve from heterostructure of two-dimensional hexagonal crystals
• Elementary band representations for the single-particle Green's function of interacting topological insulators
• Topological phase transitions with SO(4) symmetry in (2+1)d interacting Dirac fermions
• Antiferromagnetic Chern insulator with large charge gap in heavy transition-metal compounds
• Topological property of a $t_{2g}^5$ system with a honeycomb lattice structure
• Quasiparticle picture of topological phase transitions induced by interactions
• Hall conductivity as the topological invariant in magnetic Brillouin zone in the presence of interactions
• Topological charge excitations and Green's function zeros in paramagnetic Mott insulators
• Real-space topology and charge order in the Haldane-Holstein Model
• Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism
• Topological phase transition driven by Hatsugai-Kohmoto interaction on the Kagome lattice
• Combined spontaneous symmetry-breaking and symmetry-protected topological order from cluster charge interaction