Strong-weak coupling self-duality in the two-dimensional quantum phase transition of $p+ip$ superconducting arrays

TL;DR

This paper investigates a 2D quantum phase transition in a lattice of $p+ip$ superconductors, revealing a strong-weak coupling self-duality that elucidates nonperturbative effects and relates to classical dualities like Kramers-Wannier.

Contribution

It introduces an exactly solvable lattice model with four-body interactions exhibiting self-duality, extending classical dualities to many-spin interactions in higher dimensions.

Findings

Exact lattice self-duality of the 3D classical model

Connection between quantum phase transition and classical dualities

Analysis of excitation spectrum in different phases

Abstract

The 2D quantum phase transition that occurs in a square lattice of $p+ip$ superconductors is used to show how four-body interactions in $d=2$ reproduce nonperturbative effects familiar from the study of two-body interactions in $d=1$. This model can be analyzed using an exact lattice self-duality of the associated 3D classical model; this duality is the 3D generalization of the Kramers-Wannier duality of the 2D Ising model, and there are similar exact dualities for certain many-spin interactions in dimensions $d \geq 3$. We also discuss the excitation spectrum in the ordered and disordered phases, and the relationship between our model and previously studied metallic behavior of boson models with four-boson interactions.