Various static spin-correlation functions and the weights of the spin excitations, or collective normal modes, in the van Hove response function, observed in neutron scattering experiments, are calculated as a function of temperature for a model quantum-spin chain. The spins interact through an isotropic Heisenberg exchange that extends to nearest-neighbour spins. In our model, spins of magnitude 1/2 form a dimerized chain with alternating exchange interactions. We explore the static and dynamic properties for ferromagnetic and antiferromagnetic exchange interactions. Results for the various properties are shown to be exact in the limit of a high temperature, and we argue that the results are very good at low temperatures. Unlike the case for linear spin-wave theory, the results are also exact in the limit of strong dimerization, i.e. non-interacting coupled pairs of spins.Various static spin-correlation functions and the weights of the spin excitations, or collective normal modes, in the van Hove response function, observed in neutron scattering experiments, are calculated as a function of temperature for a model quantum-spin chain. The spins interact through an isotropic Heisenberg exchange that extends to nearest-neighbour spins. In our model, spins of magnitude 1/2 form a dimerized chain with alternating exchange interactions. We explore the static and dynamic properties for ferromagnetic and antiferromagnetic exchange interactions. Results for the various properties are shown to be exact in the limit of a high temperature, and we argue that the results are very good at low temperatures. Unlike the case for linear spin-wave theory, the results are also exact in the limit of strong dimerization, i.e. non-interacting coupled pairs of spins.

Journal of Physics Condensed MatterJul 20, 19981 citation

Quantum Spin Chains: Phase Behaviour and Dynamic Excitations

Jill C. Bonner, John B. Parkinson

Springer series in solid-state sciencesJan 1, 19840 citations

Transfer-Matrix Simulations of Linear Magnetic Systems

R. Matysiak, Alvaro Caramico D’Auria, Francesco Esposito +1 more

The quantum transfer-matrix method was applied to study the finite--temperature static properties of the spin S = 1 antiferromagnetic Heisen- berg chains in a wide range of the single-ion anisotropy and temperatures.The high-resolution quantum transfer-matrix simulation data are obtained for the zero-field susceptibility, specific heat as well as for the field-dependent magnetization.The microscopic parameters of a number of real quasi-one--dimensional compounds are found from fitting procedures, some theoretical approaches are numerically verified and an extension of the technique to a non-uniform bond alternating molecular magnets is ałso put forward.The quantum transfer-matrix method was applied to study the finite--temperature static properties of the spin S = 1 antiferromagnetic Heisen- berg chains in a wide range of the single-ion anisotropy and temperatures.The high-resolution quantum transfer-matrix simulation data are obtained for the zero-field susceptibility, specific heat as well as for the field-dependent magnetization.The microscopic parameters of a number of real quasi-one--dimensional compounds are found from fitting procedures, some theoretical approaches are numerically verified and an extension of the technique to a non-uniform bond alternating molecular magnets is ałso put forward.

Acta Physica Polonica AMay 1, 20000 citations

Dynamic properties of quantum spin chains: Simple route to complex behavior

Taras Verkholyak, Oleg Derzhko, Taras Krokhmalskii +1 more

We examine dynamic structure factors of spin- $1∕2$ chains with nearest-neighbor interactions of $XX$ and Dzyaloshinskii-Moriya type and with periodic and random changes in the sign of these interactions. This special kind of inhomogeneity can be eliminated from the Hamiltonian by suitable transformation of the spin variables. As a result, the dynamic structure factors of periodic or random chains can be computed from those of the uniform chains. Using the exact analytical and precise numerical results available for the uniform systems, we illustrate the effects of regular alternation or random disorder on dynamic structure factors of quantum spin chains.We examine dynamic structure factors of spin-$1∕2$ chains with nearest-neighbor interactions of $XX$ and Dzyaloshinskii-Moriya type and with periodic and random changes in the sign of these interactions. This special kind of inhomogeneity can be eliminated from the Hamiltonian by suitable transformation of the spin variables. As a result, the dynamic structure factors of periodic or random chains can be computed from those of the uniform chains. Using the exact analytical and precise numerical results available for the uniform systems, we illustrate the effects of regular alternation or random disorder on dynamic structure factors of quantum spin chains.

arXiv:0802.0389Physical Review BOct 15, 200715 citations

Quantum spin chains: Simple models with complex dynamics

Gerhard M�ller

The European Physical Journal BJun 1, 19876 citations

We examine dynamic structure factors of spin-

1∕2

chains with nearest-neighbor interactions of

XX

and Dzyaloshinskii-Moriya type and with periodic and random changes in the sign of these interactions. This special kind of inhomogeneity can be eliminated from the Hamiltonian by suitable transformation of the spin variables. As a result, the dynamic structure factors of periodic or random chains can be computed from those of the uniform chains. Using the exact analytical and precise numerical results available for the uniform systems, we illustrate the effects of regular alternation or random disorder on dynamic structure factors of quantum spin chains.