Analytical approach for the Mott transition in the Kane-Mele-Hubbard model

Abstract

The description of interactions in strongly-correlated topological phases of matter remains a challenge. Here, we develop a stochastic functional approach for interacting topological insulators including both charge and spin channels. We find that the Mott transition of the Kane-Mele-Hubbard model may be described by the variational principle with one equation. We present different views of this equation from the electron Green's function, the free-energy and the Hellmann-Feynman theorem. The band gap remains finite at the transition and the Mott phase is characterized by antiferromagnetism in the $x-y$ plane. The interacting topological phase is described through a ${\mathbb{Z}}_2$ number related to helical edge modes. Our results then show that improving stochastic approaches can give further insight on the understanding of interacting phases of matter.

12 pages, 5 figures

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Cited by in corpus (5)

• Global and Local Topological Quantized Responses from Geometry, Light and Time
• Hubbard model on the kagome lattice with time-reversal invariant flux and spin-orbit coupling
• Spin Hall conductivity in the Kane-Mele-Hubbard model at finite temperature
• Flat-band ferromagnetism in a correlated topological insulator on a honeycomb lattice
• Quantum Hall and Light Responses in a 2D Topological Semimetal