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Physical Review B

Dynamical characteristics of frustrated quantum spin chains

Andrei A. Zvyagin

Published Mar 13, 2006• 5 citations
Publisher

Abstract

Motivated by recent experiments on quasi-one-dimensional spin-frustrated quantum spin systems, we study the dynamic properties of exactly solvable quantum spin models with spin frustration. The ground-state dynamic structure factor, static structure factor (important for the neutron scattering), inhomogeneous static magnetic susceptibility, etc., are calculated. The results differ strongly from the behavior of similar characteristics of a standard Heisenberg quantum spin chain. We believe that the obtained behavior of the mentioned characteristics is generic for quantum spin chains with nearest- and next-nearest-neighbor interactions.

DOI
10.1103/physrevb.73.104414

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Motivated by recent experiments on quasi-one-dimensional spin-frustrated quantum spin systems, we study the dynamic properties of exactly solvable quantum spin models with spin frustration. The ground-state dynamic structure factor, static structure factor (important for the neutron scattering), inhomogeneous static magnetic susceptibility, etc., are calculated. The results differ strongly from the behavior of similar characteristics of a standard Heisenberg quantum spin chain. We believe that the obtained behavior of the mentioned characteristics is generic for quantum spin chains with nearest- and next-nearest-neighbor interactions.
In the framework of the exactly solvable model, using nonperturbative methods, the temperature and magnetic field behavior of the NMR relaxation rate (and low-energy dynamical structure factor) for the antiferromagnetic Heisenberg spin-1/2 chain with magnetic impurities is calculated. For a single magnetic impurity, totally screened at low temperatures by spinons of the chain, the critical exponents, which determine the low-temperature and magnetic field behavior, get renormalized. For the finite concentration of impurities with the random distribution of the impurity-chain coupling the weak disorder in the distribution does not produce essential changes to the dynamical structure factor. Contrary, the strong disorder yields drastically different behavior of the low-energy dynamical characteristics, comparing to the homogeneous chain. Our results are generic, and they qualitatively agree in limiting cases with the results of perturbative calculations for disordered spin chains and with the data of experiments on quasi-one-dimensional spin compounds.
One dimensional quantum magnets have always been an active area of research due to their experimental realizability and the rich physics that they offer. By including geometrical frustration and additional interactions, it leads to even more novel and exotic quantum phases. In this thesis, we present the results of our investigations conducted by extending the quantum systems to spin–1. We conducted static, topological and dynamical calculations numerically on the spin–1 Heisenberg chain with Dzyaloshinskii–Moriya interaction in a uniform magnetic field in the form of a spin–1 Heisenberg chain in a helical magnetic field as well as the spin–1 Heisenberg model on the spin diamond and orthogonal dimer lattices. For the spin–1 Heisenberg chain in a helical field, we obtained the phase diagram using the density matrix renormalization group method and showed conclusively that the helical field destroys any topological order. We also obtained the dynamical spin structure factor spectra to study the magnon band structures and the softening of the modes near phase transitions. We then investigated the spin–1 Heisenberg model on the spin diamond and orthogonal dimer lattices using both exact diagonalization and the density matrix renormalization group method. We obtained the phase diagrams for both systems and explicitly calculated the magnetization, static spin structure and topological order of the different phases. Similar to the spin–1 Heisenberg chain in a helical magnetic field, we also obtained the dynamical spin structure factor spectra to study the characteristics of the lowest excitation occurring in both quantum systems.
We present low-temperature static and dynamic properties of the quantum one-dimensional isotropic integer spin Heisenberg magnet with antiferromagnetic nearest-neighbour (nn) and next-nearest-neighbour (nnn) interactions. The modified spin-wave theory is used to provide quantities such as the spin-wave dispersion relation, the ground-state energy, the gap and its dependence with temperature, and the asymptotic behaviour of the spin–spin correlation function. The ground state energy and the singlet–triplet energy gap are obtained for several values of j, defined as the ratio of the nnn interaction constant to the nn one. Our results show that the ground-state and the gap energies increase with j, in accordance with numerical results available in the literature. The calculation of the dynamic correlation function is performed using the projection operator formalism: the procedure includes up to two-magnon processes. We show that, depending on the values of the frustration parameter j, the wavevector and the temperature, a double-peak structure for the dynamical correlation function can develop.
We examine dynamic structure factors of spin-1∕21∕21∕2 chains with nearest-neighbor interactions of XXXXXX 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.
Interactions between elementary excitations in quasi-one-dimensional antiferromagnets are of experimental relevance and their quantitative theoretical treatment has been a theoretical challenge for many years. Using matrix product states, one can explicitly determine the wave functions of the one- and two-particle excitations, and, consequently, the contributions to dynamical correlations. We apply this framework to the (nonintegrable) frustrated dimerized spin-1/2 chain, a model for generic spin-Peierls systems, where low-energy quasiparticle excitations are bound states of topological solitons. The spin structure factor involving two quasiparticle scattering states is obtained in the thermodynamic limit with full momentum and frequency resolution. This allows very subtle features in the two-particle spectral function to be revealed which, we argue, could be seen, e.g., in inelastic neutron scattering of spin-Peierls compounds under a change of the external pressure.
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.