Majorana lattice gauge theory: symmetry breaking, topological order and intertwined orders all in one

TL;DR

This paper introduces an exactly solvable Majorana lattice gauge theory that exhibits coexistence of symmetry breaking, topological order, and intertwined orders, providing insights into complex quantum phases.

Contribution

It presents a novel exactly solvable Majorana lattice gauge theory demonstrating intertwined symmetry breaking and topological order in a unified framework.

Findings

Ground state exhibits coexistence of symmetry breaking and topological order.

Z2 symmetry breaking leads to intertwined antiferromagnetic and eta-pairing orders.

Topological order characterized by Z2 quantum spin liquid state.

Abstract

The Majorana lattice gauge theory purely composed of Majorana fermions on square lattice is studied throughly. The ground state is obtained exactly and exhibits the coexistence of symmetry breaking and topological order. The $Z_2$ symmetry breaking of matter fields leads to the intertwined antiferromagnetic spin order and $\eta$-pairing order. The topological order is reflected in the $Z_2$ quantum spin liquid ground state of gauge fields. The Majorana lattice gauge theory, alternatively can be viewed as interacting Majorana fermion model, is possibly realized on a Majorana-zero-mode lattice.