Reflections on the One Dimensional Realization of Odd-Frequency Pairing

TL;DR

This paper explores the realization of odd-frequency pairing correlations in a one-dimensional Kondo lattice, identifying their properties and discussing their evolution into long-range order in higher dimensions.

Contribution

It introduces a lattice model that captures the continuum theory of odd-frequency pairing and analyzes its excitation spectrum and potential for long-range order.

Findings

Identification of odd-frequency singlet pairing in the lattice model

Discovery of a spin gap and spinless excitations in the spectrum

Discussion of the transition from power-law correlations to long-range order

Abstract

We discuss the odd-frequency pairing correlations discovered by Zachar, Kivelson and Emery (ZKE) in a one dimensional Kondo lattice. A lattice model that realizes the continuum theory of ZKE is introduced and the correlations it gives rise to are identified as odd-frequency singlet pairing. The excitation spectrum is found to contain a spin gap, and a much lower energy band of spinless excitations. We discuss how the power-law correlations realized in the ZKE model evolve into true long-range order when Kondo chains are weakly coupled together and tentatively suggest a way in which the higher dimensional model can be treated using mean-field theory.