Long-range order in quantum spin systems : a rigorous argument

The $T=0$ dynamics of a family of one-dimensional quantum spin systems with fully ordered (ferromagnetic or spin-flop) ground states is investigated. By rigorous calculations, it is demonstrated that the $T=0$ dynamic structure factor is, in general, not a $\ensuremath{\delta}$ function as predicted by linear spin-wave theory but characterized by more complicated structures with nonzero linewidths. The exact result approaches the spin-wave result in the classical limit $s\ensuremath{\rightarrow}\ensuremath{\infty}$. The results of this study demonstrate how quantum effects may invalidate spin-wave theory even in the presence of saturated magnetic long-range order. Hence the failure of spin-wave theory is not necessarily linked to the absence or strong reduction of long-range order typical for one-dimensional quantum spin systems. The unreliability of spin-wave theory has therefore to be suspected also for the dynamics of three-dimensional quantum spin systems where the long-range order is always strong at $T=0$ .The $T=0$ dynamics of a family of one-dimensional quantum spin systems with fully ordered (ferromagnetic or spin-flop) ground states is investigated. By rigorous calculations, it is demonstrated that the $T=0$ dynamic structure factor is, in general, not a $\ensuremath{\delta}$ function as predicted by linear spin-wave theory but characterized by more complicated structures with nonzero linewidths. The exact result approaches the spin-wave result in the classical limit $s\ensuremath{\rightarrow}\ensuremath{\infty}$. The results of this study demonstrate how quantum effects may invalidate spin-wave theory even in the presence of saturated magnetic long-range order. Hence the failure of spin-wave theory is not necessarily linked to the absence or strong reduction of long-range order typical for one-dimensional quantum spin systems. The unreliability of spin-wave theory has therefore to be suspected also for the dynamics of three-dimensional quantum spin systems where the long-range order is always strong at $T=0$.

Physical review. B, Condensed matterAug 1, 198329 citations

and Long Range Order in Quantum Field Theory

Francesco Guerra

Jan 1, 19760 citations

Long-Range Order in Ideal Ferromagnets

Masuo Suzuki

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

Peierls Argument and Long-Range Order Behavior of Quantum Lattice Systems with Unbounded Spins

Sergio A Albeverio, A. Yu. Kondratiev, A. L. Rebenko

Journal of Statistical PhysicsSep 1, 199813 citations

Characterization of exotic orders in quantum spin systems

俊輔古川

Jan 1, 20071 citation

The

T=0

dynamics of a family of one-dimensional quantum spin systems with fully ordered (ferromagnetic or spin-flop) ground states is investigated. By rigorous calculations, it is demonstrated that the

T=0

dynamic structure factor is, in general, not a $\ensuremath{\delta}$ function as predicted by linear spin-wave theory but characterized by more complicated structures with nonzero linewidths. The exact result approaches the spin-wave result in the classical limit $s\ensuremath{\rightarrow}\ensuremath{\infty}$. The results of this study demonstrate how quantum effects may invalidate spin-wave theory even in the presence of saturated magnetic long-range order. Hence the failure of spin-wave theory is not necessarily linked to the absence or strong reduction of long-range order typical for one-dimensional quantum spin systems. The unreliability of spin-wave theory has therefore to be suspected also for the dynamics of three-dimensional quantum spin systems where the long-range order is always strong at

T=0