Fermion Condensation and Gapped Domain Walls in Topological Orders

TL;DR

This paper introduces fermion condensation in 2D topological orders, describing it as gapped domain walls that enable phase transitions from bosonic to fermionic orders, with a hierarchical decomposition and comprehensive rules.

Contribution

It generalizes boson condensation to fermion condensation, establishing a hierarchy principle and developing a complete set of rules for fermion condensation in topological orders.

Findings

Fermion condensation can be decomposed into boson and minimal fermion condensation.

A hierarchy principle governs fermion condensation processes.

An exact mapping exists between bosonic and fermionic topological orders via gapped domain walls.

Abstract

We propose the concept of fermion condensation in bosonic topological orders in two spatial dimensions. Fermion condensation can be realized as gapped domain walls between bosonic and fermionic topological orders, which are thought of as a real-space phase transitions from bosonic to fermionic topological orders. This generalizes the previous idea of understanding boson condensation as gapped domain walls between bosonic topological orders. We show that generic fermion condensation obeys a Hierarchy Principle by which it can be decomposed into a boson condensation followed by a minimal fermion condensation, which involves a single self-fermion that is its own anti-particle and has unit quantum dimension. We then develop the rules of minimal fermion condensation, which together with the known rules of boson condensation, provides a full set of rules of fermion condensation. Our studies point to an exact mapping between the Hilbert spaces of a bosonic topological order and a fermionic topological order that share a gapped domain wall.