Discrete Shift and Polarization from Response to Symmetry Defects in Interacting Topological Phases

TL;DR

This paper extends the study of crystalline symmetry-protected topological invariants to interacting systems, using DMRG to analyze defects in a Hofstadter model, revealing quantized topological invariants in different phases.

Contribution

It introduces an interacting Hofstadter model with symmetry defects and demonstrates the quantization of topological invariants in correlated regimes using DMRG.

Findings

Topological invariants remain quantized in both phases.

Quantitative extraction of topological quantities using DMRG.

Model realizes Chern insulator and charge density wave states.

Abstract

We extend the previous study of extracting crystalline symmetry-protected topological invariants to the correlated regime. We construct the interacting Hofstadter model defined on square lattice with the rotation and translation symmetry defects: disclination and dislocation. The model realizes Chern insulator and the charge density wave state as one tunes interactions. Employing the density matrix renormalization group (DMRG) method, we calculate the excess charge around the defects and find that the topological invariants remain quantized in both phases, with the topological quantity extracted to great precision. This study paves the way for utilizing matrix product state, and potentially other quantum many-body computation methods, to efficiently study crystalline symmetry defects on 2D interacting lattice systems.