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

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 one-dimensional, periodic Heisenberg, inverse square exchange, and XY models we give numerical evidence for the hidden ODLRO conjectured by Anderson. A connection to the singlet pair correlations in one-dimensional models of interacting electrons is made and briefly discussed.