Plateaux Transitions in the Pairing Model:Topology and Selection Rule

TL;DR

This paper investigates topological phase transitions in a 2D lattice fermion pairing model, highlighting the role of topological invariants, vortices, and edge states, with numerical analysis of disorder effects.

Contribution

It introduces a topological classification of pairing states, details the selection rule for phase transitions, and explores edge states and disorder effects in the model.

Findings

Phases are labeled by topological integers with vortex structures.

Transitions follow a specific selection rule based on topological invariants.

Edge states reflect the bulk's topological nature and are affected by randomness.

Abstract

Based on the two-dimensional lattice fermion model, we discuss transitions between different pairing states. Each phase is labeled by an integer which is a topological invariant and characterized by vortices of the Bloch wavefunction. The transitions between phases with different integers obey a selection rule. Basic properties of the edge states are revealed. They reflect the topological character of the bulk. Transitions driven by randomness are also discussed numerically.