A diagnosis of explicit symmetry breaking in the tight-binding constructions for symmetry-protected topological systems

Abstract

It has been well established that for symmetry protected topological systems, the non-trivial topology prevents a real space representation using exponentially localized Wannier wavefunctions (WFs) in all directions, unless the protecting symmetry is sacrificed as an on-site transformation. This makes it challenging to determine the symmetry of various physical observables represented using such WFs. In this work, we propose a practical method for overcoming such challenges using the Kane-Mele model as a concrete example. We present a systematic procedure for diagnosing the symmetry of any observables, as well as a method for constructing symmetric operators up to arbitrary truncation accuracy.

6 pages + 5 figures

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Cited by in corpus (8)

• Efficient simulation of moire materials using the density matrix renormalization group
• Realization of Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model
• Lattice model for the Coulomb interacting chiral limit of the magic angle twisted bilayer graphene: symmetries, obstructions and excitations
• DMRG study of strongly interacting ${\mathbb{Z}}_2$ flatbands: a toy model inspired by twisted bilayer graphene
• Chiral $p$-wave superconductivity in twisted bilayer graphene from dynamical mean field theory
• Correlated Insulators in Twisted Bilayer Graphene
• Revisiting Bloch electrons in magnetic field: Hofstadter physics via hybrid Wannier states
• Real space representation of topological system: twisted bilayer graphene as an example