Topological and magnetic properties of the interacting Bernevig-Hughes-Zhang model

We explore the influence of electronic correlations on the Bernevig-Hughes-Zhang model using the real-space density matrix renormalization group (DMRG) algorithm. By incorporating the complete multi-orbital Hubbard interaction, we construct a magnetic and topological phase diagram as a function of gap parameter (m) and the Hubbard interaction strength (U) through exact DMRG simulations on N × 4 cylinders [1]. Our analysis confirms the persistence of the topological phase in the presence of interactions, consistent with prior DMFT studies [2]. Additionally, it also uncovers an intriguing phase transition from a paramagnetic topological insulator to an antiferromagnetic topological insulator. To supplement these results, we also performed an unsupervised machine learning methodology that analyzes the orbital structure of the real-space edges and confirms our DMRG phase diagram.

[1] R. Soni, H. Radhakrishnan, B. Rosenow, G. Alvarez, and A. Del Maestro, to be submitted.

[2] J. C. Budich, B. Trauzettel, and G. Sangiovanni, Phys. Rev. B 87, 235104 (2013).