Edge Reconstruction in a Quantum Spin Hall Insulator

Rahul Soni, Matthias Thamm, Gonzalo Alvarez, Bernd Rosenow, and Adrian Del Maestro

arXiv:2508.10726

Abstract

We study interaction-driven edge reconstruction in a quantum spin Hall insulator described by the BHZ model with Kanamori–Hubbard interactions using real-space density matrix renormalization group method in both the grand-canonical and canonical ensembles. For a two-dimensional cylinder with one smooth edge, we identify discrete particle-number transitions that lead to spin-polarized edge states stabilized by an emergent ferromagnetic exchange interaction. The reconstruction is orbital-selective, occurring predominantly in the $s$-orbital channel. Our results reveal a fully microscopic mechanism for emergent spin polarization at the edge that could compromise the topological protection of helical edge states by time reversal symmetry.

Description

This repository includes links, code, scripts, and data to generate the figures in a paper.

Requirements

The data in this project is generated using three different methods: Exact Diagonalization, Mean-Field and DMRG. Processed data is included in the data directory.

1. The spectral data for the interacting BHZ model was generated via self-consistent real-space mean-field calculations. The code can be found here. Detail instructions are provided in this repo regarding compilations, executions and more.

2. The real space charge, magnetic, exact ground-state data for interacting BHZ ladders was generated via DMRG for both canonical and grand-canonical ensemble. For the large DMRG calculations we considered two different codes (benchmarked against each other). The full raw data set can be found on zenodo: .

   (a) The in-house DMRG++ software developed by G.A. The documentation for the same is provided here, for compilation follow the steps below:

   DMRG++ Code and Compilation

   git clone https://code.ornl.gov/gonzalo_3/PsimagLite.git
   cd PsimagLite/lib
   perl configure.pl
   make
   cd ../../
   git clone https://code.ornl.gov/gonzalo_3/dmrgpp.git
   cd dmrgpp/src
   perl configure.pl
   make

   Dependencies include the BOOST, HDF5 and OpenBLAS libraries

   Running the Code

   This will generate dmrg and observe executables. Run the dmrg executable first to save the ground state and then use the observe executable to evaluate all the necessary observables.

   (b) the ITensors DMRG code available here using the ITensor.jl package. To run the code, clone the repository

   git clone https://github.com/DelMaestroGroup/BHZ_DMRG_Julia.git

   Running the code requires Julia 1.11.1 or higher:

   julia ./BHZitensorsDMRG/run_bhz.jl ARGS KWARGS

   For details, see README of the repository.

3. For small system we considered the many-body exact diagonalization code. The code can be found here. Detail instructions are provided in this repo regarding compilations, executions and more.

Support

The creation of these materials was supported in part by the Department of Energy under Award No. DE-SC0022311.

Figures

Figure 1: Lattice Geometry and Potential Profile

Figure 2: Mean-field Orbital and Spin Resolved Spectral Function

Figure 3: Total particles versus Confining potential

Figure 4: GSE for different Sz sectors of $N_0$, $N_0+1$ and $N_0+2$ particle sectors

Figure 5: Change in particle density between different particle sectors

Figure 6: Magnetization profiles for the ground-states

Supplementary Figure 1: Spectral comparison for different helical potential

Supplementary Figure 2: Finite size scaling of the exchange coupling

This figure is relesed under CC BY-SA 4.0 and can be freely copied, redistributed and remixed.