An attempt is made to investigate the relation between (diagonal) long-range order (LRO or spontaneous magnetization in spin systems) and off-diagonal long-range order (ODLRO or long-range correlation in spin systems). It is shown that ODLRO cannot exceed LRO in ideal ferromagnets under some plausible conditions. Several kinds of long-range order and their mutual relations are also discussed in ideal ferromagnets whose total spin commutes with the Hamiltonian. It is also argued that neither LRO or ordinary ODLRO exists in the two-dimensional ferromagnetic Heisenberg model. However, a possibility is proposed that other kinds of ODLRO exist in the case of higher spin for such a system. The Heisenberg model with long-range interaction is exemplified, and it is pointed out that the total spin, instead of the total magnetization, should be taken as an order parameter in phenomenological arguments of the Heisenberg model.An attempt is made to investigate the relation between (diagonal) long-range order (LRO or spontaneous magnetization in spin systems) and off-diagonal long-range order (ODLRO or long-range correlation in spin systems). It is shown that ODLRO cannot exceed LRO in ideal ferromagnets under some plausible conditions. Several kinds of long-range order and their mutual relations are also discussed in ideal ferromagnets whose total spin commutes with the Hamiltonian. It is also argued that neither LRO or ordinary ODLRO exists in the two-dimensional ferromagnetic Heisenberg model. However, a possibility is proposed that other kinds of ODLRO exist in the case of higher spin for such a system. The Heisenberg model with long-range interaction is exemplified, and it is pointed out that the total spin, instead of the total magnetization, should be taken as an order parameter in phenomenological arguments of the Heisenberg model.

Progress of Theoretical PhysicsNov 1, 196912 citations

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

J. C. Talstra, Steven P. Strong, P. W. Anderson

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 $\mathrm{XY}$ 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.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 $\mathrm{XY}$ 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.

arXiv:cond-mat/9411074Physical Review LettersJun 26, 199521 citations

A rigorous theorem on off-diagonal long-range order of boson systems

Guang-Shan Tian

For a strongly interacting boson system, it has been proposed that the concept of off-diagonal long-range ordering (ODLRO) is equivalent to Bose-Einstein condensation for a free boson system. Therefore, the existence of ODLRO in the ground state implies superfluidity. The author checks the validity of this proposition from another point of view. He rigorously shows that, for a hard-core lattice-boson system with a short-ranged interaction ODLRO is suppressed when a charged excitation gap develops and, hence, the boson system becomes a Mott-insulator. Finally, by using his theorem, he shows some interesting properties of the antiferromagnetic Heisenberg model, which can be taken as a hard-core lattice-boson system.For a strongly interacting boson system, it has been proposed that the concept of off-diagonal long-range ordering (ODLRO) is equivalent to Bose-Einstein condensation for a free boson system. Therefore, the existence of ODLRO in the ground state implies superfluidity. The author checks the validity of this proposition from another point of view. He rigorously shows that, for a hard-core lattice-boson system with a short-ranged interaction ODLRO is suppressed when a charged excitation gap develops and, hence, the boson system becomes a Mott-insulator. Finally, by using his theorem, he shows some interesting properties of the antiferromagnetic Heisenberg model, which can be taken as a hard-core lattice-boson system.

Journal of Physics A Mathematical and GeneralMay 21, 19925 citations

\mathrm{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.