New Types of Off-Diagonal Long Range Order in Spin-Chains

TL;DR

This paper explores new forms of off-diagonal long-range order in spin chains, providing numerical and rigorous evidence for hidden ODLRO in various models, and connecting it to electron pair correlations.

Contribution

It introduces novel types of ODLRO involving operators that modify the chain, with strong numerical and analytical support for these phenomena.

Findings

Strong numerical evidence for hidden ODLRO in Heisenberg and Inverse Square Exchange models.

Rigorous demonstration of ODLRO in the XY model and free fermions.

Connection established between ODLRO and singlet pair correlations in 1D electron models.

Abstract

We discuss new possibilities for Off-Diagonal Long Range Order (ODLRO) in spin chains involving operators which add or delete sites from the chain. For the Heisenberg and Inverse Square Exchange models we give strong numerical evidence for the hidden ODLRO conjectured by Anderson \cite{pwa_conj}. We find a similar ODLRO for the XY model (or equivalently for free fermions in one spatial dimension) which we can demonstrate rigorously, as well as numerically. A connection to the singlet pair correlations in one dimensional models of interacting electrons is made and briefly discussed.