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Physical review. B./Physical review. B

Topological edge states and impurities: Manifestation in the local static and dynamical characteristics of dimerized quantum chains

Andrei A. Zvyagin

Published Apr 17, 2018• 2 citations
Publisher

Abstract

Based on the results of exact analytic calculations, we show that topological edge states and impurities in quantum dimerized chains manifest themselves in various local static and dynamical characteristics, which can be measured in experiments. In particular, topological edge states can be observed in the magnetic field behavior of the local magnetization or magnetic susceptibility of dimerized spin chains as jumps (for the magnetization) and features (for the static susceptibility) at zero field. In contrast, impurities reveal themselves in similar jumps and features, however, at nonzero values of the critical field. We also show that dynamical characteristics of dimerized quantum chains also manifest the features, related to the topological edge states and impurities. Those features, as a rule, can be seen more sharply than the manifestation of bulk extended states in, e.g., the dynamical local susceptibility. Such peculiarities can be observed in one-dimensional dimerized spin chains, e.g., in NMR experiments, or in various realizations of quantum dimerized chains in optical experiments.

DOI
10.1103/physrevb.97.144412

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Based on the results of exact analytic calculations, we show that topological edge states and impurities in quantum dimerized chains manifest themselves in various local static and dynamical characteristics, which can be measured in experiments. In particular, topological edge states can be observed in the magnetic field behavior of the local magnetization or magnetic susceptibility of dimerized spin chains as jumps (for the magnetization) and features (for the static susceptibility) at zero field. In contrast, impurities reveal themselves in similar jumps and features, however, at nonzero values of the critical field. We also show that dynamical characteristics of dimerized quantum chains also manifest the features, related to the topological edge states and impurities. Those features, as a rule, can be seen more sharply than the manifestation of bulk extended states in, e.g., the dynamical local susceptibility. Such peculiarities can be observed in one-dimensional dimerized spin chains, e.g., in NMR experiments, or in various realizations of quantum dimerized chains in optical experiments.
The characteristics of the nuclear magnetic resonance (NMR), the contributions to the spin-lattice relaxation rate, and Knight shift of the resonance position are calculated exactly for a model spin-1/21/21/2 XYXYXY chain with the magnetic impurity. It is shown that the deviations of the impurity's coupling to the chain and the effective impurity's ggg factor from the values in the host spin chain yield special features in the temperature and magnetic field behavior for these NMR characteristics. The role of impurity-induced local levels in the NMR low-energy spin dynamics of spin chains is determined.
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.
In this work we consider several exactly solvable models of magnetic impurities in critical quantum antiferromagnetic spin chains and multichannel Kondo impurities. Their ground-state properties are studied, and the finite set of nonlinear integral equations which exactly describe the thermodynamics of the models is constructed. We obtain several analytical low-energy expressions for the temperature, magnetic field, and frequency dependences of important characteristics of exactly solvable disordered quantum spin models and disordered multichannel Kondo impurities with essential many-body interactions. We show that the only low-energy parameter that gets renormalized is the velocity of the low-lying excitations (or the effective crossover scale connected with each impurity); the others appear to be universal. In our study several kinds of strong disorder important for experiments were used. Some of them produce low divergences in certain characteristics of our strongly disordered critical systems (compared with finite values for the homogeneous case or a single impurity). For weak disorder, or for narrow distributions of the local Kondo temperatures, our exact results reveal the presence of Kondo screening of disordered ensembles of magnetic impurities by low-lying excitations of the host. We point out that our results qualitatively coincide with the data of experiments on real disordered quasi-one-dimensional antiferromagnetic systems and with the similar behavior of some heavy metallic alloys.