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

• Published in: arXiv.org
• Main Authors: Soni, Rahul, Radhakrishnan, Harini, Rosenow, Bernd, Alvarez, Gonzalo, Adrian Del Maestro
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 14.09.2024
• Subjects: Algorithms; Antiferromagnetism; Correlation; Machine learning; Magnetic moments; Magnetic properties; Magnetic structure; Phase diagrams; Phase transitions; Physics - Strongly Correlated Electrons; Space density; Structure factor; Topological insulators; Topology; Unsupervised learning
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2310.17614

We investigate the effects of electronic correlations on the Bernevig-Hughes-Zhang model using the real-space density matrix renormalization group (DMRG) algorithm. We introduce a method to probe topological phase transitions in systems with strong correlations using DMRG, substantiated by an unsupervised machine learning methodology that analyzes the orbital structure of the real-space edges. Including the full multi-orbital Hubbard interaction term, we construct a phase diagram as a function of a gap parameter (\(m\)) and the Hubbard interaction strength (\(U\)) via exact DMRG simulations on \(N\times 4\) cylinders. Our analysis confirms that the topological phase persists in the presence of interactions, consistent with previous studies, but it also reveals an intriguing phase transition from a paramagnetic to a stripey antiferromagnetic topological insulator. The combination of the magnetic structure factor, strength of magnetic moments, and the orbitally resolved density, provides real-space information on both topology and magnetism in a strongly correlated system.