Low-energy Physics in Low-dimensional Gapped Quantum Spin Systems

貴則 杉本

Indrani Bose

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.

K.-H. Mütter

J. Richert

We develop a variational formalism in order to study the structure of low energy spectra of frustrated quantum spin systems. It is first applied to trial wavefunctions of ladders with one spin-1/2 on each site. We determine energy minima of these states. The variational ground state shows a finite energy gap with respect to the energies of states which span the Hilbert space and are orthogonal to it. This is the case for any size of the system. Under some justifiable approximations the argument can be extended to even-legged ladder systems in 2d and higher dimensional spaces. The Hamiltonian can contain spin-spin coupling interactions of any range. For specific values of the coupling strengths level degeneracies can occur.

Akira Kawaguchi, Tatsuya Fujii, Norio Kawakami

Magnetic properties of a one-dimensional multicomponent quantum-spin system with an excitation gap are studied based on the integrable spin model introduced by Bariev et al. [Z. Phys. B 96, 395 (1995)]. By exactly computing the magnetization, we show how a characteristic structure with plateaus and cusps appears in the magnetization process. To study the low-energy dynamics of the system, we apply a finite-size scaling analysis to the excitation spectrum, and thereby evaluate the power-law exponent as well as the enhancement factor for the low-temperature NMR relaxation rate ${1/T}_{1}.$ We discuss the critical properties of ${1/T}_{1}$ around plateaus and cusps in the magnetization curve.

P. Lemmens, M. Fischer, M. Grove +5 more