Equality of bulk wave functions and edge correlations in topological superconductors: A spacetime derivation

TL;DR

This paper demonstrates why, in certain topological superconductors, the bulk wavefunctions are exactly equal to edge correlation functions, using a spacetime derivation involving Euclidean rotation and Lorentz invariance.

Contribution

It provides a spacetime-based derivation explaining the equality of bulk wavefunctions and edge correlations in topological superconductors, extending to higher dimensions and correlated states.

Findings

Bulk wavefunctions equal edge correlations in certain topological superconductors

Euclidean rotation links bulk wavefunctions to edge correlations

Method extends to higher dimensions and fractionalized states

Abstract

For certain systems, the N-particle ground-state wavefunctions of the bulk happen to be exactly equal to the N-point space-time correlation functions at the edge, in the infrared limit. We show why this had to be so for a class of topological superconductors, beginning with the p+ip state in D=2+1. Varying the chemical potential as a function of Euclidean time between weak and strong pairing states is shown to extract the wavefunction. Then a Euclidean rotation that exchanges time and space and approximate Lorentz invariance lead to the edge connection. We illustrate straightforward extension to other dimensions (eg. 3He- B phase in D=3+1) and to correlated states like fractionalized topological superconductors.