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Journal of Physics Condensed Matter

Reflectionless spin waves in Heisenberg chains with spin impurity segments

S. N. Evangelou, Anzhong Wang, Sang Xiong

Published Jun 27, 1994• 16 citations
Publisher

Abstract

We study, via a scattering transfer-matrix approach, the spin waves of a Heisenberg chain with randomly inserted impurity segments having spin and coupling strength different from the host ones. Numerical results show the existence of completely unscattered reflectionless modes, whose number is sensitive to the impurity parameters. If both the spin and the coupling strength of the impurities are different from those of the host we find a novel type of resonant propagating wave, for which the reflection by a single segment is minimum but not vanishing. The relevance of the present results to other systems and to possible applications are discussed.

DOI
10.1088/0953-8984/6/26/015

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We study, via a scattering transfer-matrix approach, the spin waves of a Heisenberg chain with randomly inserted impurity segments having spin and coupling strength different from the host ones. Numerical results show the existence of completely unscattered reflectionless modes, whose number is sensitive to the impurity parameters. If both the spin and the coupling strength of the impurities are different from those of the host we find a novel type of resonant propagating wave, for which the reflection by a single segment is minimum but not vanishing. The relevance of the present results to other systems and to possible applications are discussed.
We study the thermodynamics of a one-dimensional quantum spin-1/2 Heisenberg ferromagnetic system with random antiferromagnetic impurity bonds. In the dilute impurity limit, we generalize the modified spin-wave theory for random spin chains, where local chemical potentials for spin waves in ferromagnetic spin segments are introduced to ensure zero magnetization at finite temperature. This approach successfully describes the crossover from the behavior of a pure one-dimensional ferromagnet at high temperatures to a distinct Curie behavior due to randomness at low temperatures. We discuss the effects of impurity bond strength and concentration on the crossover and low-temperature behavior.
The finite-temperature transport properties of a spin-12\frac{1}{2}21​ anisotropic Heisenberg chain with an embedded spin-SSS impurity are studied. Using primarily numerical diagonalization techniques, we study the dependence of the dynamical spin and thermal conductivities on the lattice size, the magnitude of the impurity spin, the host-impurity coupling, the easy axis anisotropy, as well as the dependence on temperature. Particularly for the temperature dependence, we discuss the screening of the impurity by the chain eventually leading to the cutting or healing of the host chain. Numerical results are supported by analytical arguments obtained in the strong host-impurity coupling regime.
We investigate the effective interaction between two localized spin impurities embedded in a frustrated spin-1/2 J1 ⁣− ⁣J2J_1\!-\!J_2J1​−J2​ Heisenberg chain. Treating the impurity spins as classical moments coupled locally to the host, we combine second--order perturbation theory with large--scale density matrix renormalization group (DMRG) calculations to determine the impurity--impurity interaction as a function of separation, coupling strength, and magnetic frustration. In the weak--coupling regime, we show that the interaction is governed by the the static spin susceptibility of the host and exhibits oscillatory power--law decay in the gapless phase, modified by universal logarithmic corrections at the SU(2)--symmetric critical point. In the gapped dimerized phase, the interaction decays exponentially with distance. For intermediate and strong impurity--host coupling, we observe a crossover to a boundary--dominated regime characterized by pronounced parity effects associated with the length of the chain segment between impurities, signaling a breakdown of the simple RKKY--like description. Our results establish impurity--impurity interactions as a sensitive probe of frustrated quantum spin liquids and provide a controlled framework for distinguishing gapless and gapped phases through local perturbations.
We investigate the effective interaction between two localized spin impurities embedded in a frustrated spin-12\frac {1}{2}21​ J1J_1J1​–J2J_2J2​ Heisenberg chain. Treating the impurity spins as classical moments coupled locally to the host, we combine second-order perturbation theory with large-scale density matrix renormalization group (DMRG) calculations to determine the impurity–impurity interaction as a function of separation, coupling strength, and magnetic frustration. In the weak-coupling regime, we show that the interaction is governed by the static spin susceptibility of the host and exhibits oscillatory power-law decay in the gapless phase, modified by universal logarithmic corrections at the SU(2)-symmetric critical point. In the gapped dimerized phase, the interaction decays exponentially with distance. For intermediate and strong impurity–host coupling, we observe a crossover to a boundary-dominated regime characterized by pronounced parity effects associated with the length of the chain segment between impurities, signaling a breakdown of the simple RKKY-like description. Our results establish impurity–impurity interactions as a sensitive probe of frustrated quantum spin liquids and provide a controlled framework for distinguishing gapless and gapped phases through local perturbations. Abstract Published by the Jagiellonian University 2026 authors
Quantum transport in a lattice is distinct from its counterpart in continuum media. Even a free wave packet travels differently in a lattice than in the continuum. We describe quantum scattering in a one-dimensional lattice and illustrate characteristics of quantum transport such as resonant transmission. In particular we examine the transport characteristics of a random trimer model. We demonstrate the real-time propagation of a wave packet and its phase shift due to impurity configurations. Spin-flip scattering is also taken into account in a spin-chain system. We show how individual spins in the chain evolve as a result of a spin-flip interaction between an incoming electron and a spin chain.
Low-lying excited states of the spin-1 antiferromagnetic Heisenberg chain with a spin- S ( S >1) impurity are investigated by means of variational method. It is shown that (1) the phenomenological Hamiltonian which may be useful in the analysis of the experimental results can be derived from the usual Hamiltonian, (2) the origin of the anisotropy in the phenomenological Hamiltonian can be explained from the results obtained by the analytical method, (3) the impurity spin brings about a massive mode in the Haldane gap, (4) the energy levels of the massive mode can be classified into four multiples corresponding to the states with the total spin quantum S = S +1, S and S -1 coupled to triplet of host-system and the state with S = S coupled to the singlet of host-system.