Triangular lattice Majorana-Hubbard model: Mean field theory and DMRG on a width-4 torus

TL;DR

This paper investigates a Majorana-Hubbard model on a triangular lattice, using mean field theory and DMRG, revealing how attractive interactions can induce phase transitions in topological states.

Contribution

It introduces a combined mean field and DMRG analysis of the Majorana-Hubbard model on a triangular lattice, highlighting interaction-driven phase transitions.

Findings

Attractive interactions induce phase transitions in the topological phase.

Mean field and DMRG methods complement each other in analysis.

The model is relevant for understanding Majorana modes in solid state systems.

Abstract

Majorana modes can arise as zero energy bound states in a variety of solid state systems. A two-dimensional phase supporting these quasiparticles, for instance, emerges on the surface of a topological superconductor with the zero modes localized at the cores of vortices. At low energies, such a setup can be modeled by Majorana modes that interact with each other on the Abrikosov lattice. In experiments, the lattice is usually triangular. Motivated by the practical relevance, we explore the phase diagram of this Hubbard-like Majorana model using a combination of mean field theory and numerical simulation of thin torus geometries through the density matrix renormalization group algorithm. Our analysis indicates that attractive interactions between Majoranas can drive a phase transition in an otherwise gapped topological state.