# Majorana-Hubbard model on the square lattice

## TL;DR

This paper investigates a Majorana-Hubbard model on a square lattice, revealing a complex phase diagram with superfluid and gapless phases, and identifies a supersymmetric transition between them.

## Contribution

It introduces a detailed analysis of the interacting Majorana modes on a square lattice, including the discovery of a superfluid phase and a supersymmetric transition.

## Key findings

- Identification of a superfluid phase with spontaneous U(1) symmetry breaking
- Discovery of a supersymmetric transition between phases
- Rich phase diagram depending on interaction strength

## Abstract

We study a tight-binding model of interacting Majorana (Hermitian) modes on a square lattice. The model may have an experimental realization in a superconducting-film--topological-insulator heterostructure in a magnetic field. We find a rich phase diagram, as a function of interaction strength, including a superfluid phase with spontaneous breaking of an emergent $U(1)$ symmetry, separated by a supersymmetric transition from a gapless normal phase.