chapter  Chapter 7
50 Pages

Low-dimensional Quantum Spin Systems

Low-dimensional quantum spin systems is interacting many body systems for which several rigorous results are known. A large number of compounds exist which can effectively be described as low-dimensional spin systems. Frustration occurs when the interaction energies associated with all the spin pairs cannot be simultaneously minimized. The parallel spin pair may be located on any one of the bonds of the triangle. The entropy/spin has a non-zero value in the ground state and there is no ordering of the spins. The sum over permutations is in accordance with the bosonic nature of the waves, the spin waves, propagating along the chain. The energy-momentum relations suggest that the low-lying spectrum is actually a combination of two elementary excitations known as spinons. In the case of integer spin chains, the spinons axe bound and the excitation spectrum consists of spin-wave-like modes exhibiting the Haldane gap.