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arXiv:cond-mat/0303565 · Physical Review Letters

Quantum Magnetic Impurities in Magnetically Ordered Systems

A. H. Castro Neto, E. Novais, L. Borda, Gergely Zaránd, Ian K. Affleck

Published Aug 26, 2003• 50 citations
arXivHTMLPDF

Abstract

We discuss the problem of a spin 1/2 impurity immersed in a spin S magnetically ordered background. We show that the problem maps onto a generalization of the dissipative two level system with two independent heat baths, associated with the Goldstone modes of the magnet, that couple to different components of the impurity spin operator. Using analytical perturbative renormalization group methods and accurate numerical renormalization group we show that contrary to other dissipative models there is quantum frustration of decoherence and quasiscaling even in the strong coupling regime. We make predictions for the behavior of the impurity magnetic susceptibility. Our results may also have relevance to quantum computation.

DOI
10.1103/physrevlett.91.096401

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We study a model of frustration of decoherence in an open quantum system. Contrary to other dissipative Ohmic impurity models, such as the Kondo model or the dissipative two-level system, the impurity model discussed here never presents overdamped dynamics even for strong coupling to the environment. We show that this unusual effect has its origins in the quantum-mechanical nature of the coupling between the quantum impurity and the environment. We study the problem using analytic and numerical renormalization group methods and obtain expressions for the frequency and temperature dependence of the impurity susceptibility in different regimes.
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
We investigate quantum impurity problems, where a local magnetic moment is coupled to the spin density of a bosonic environment, leading to bosonic versions of the standard Kondo and Anderson impurity models. In a physical situation, these bosonic environments can correspond either to deconfined spinons in certain classes of Z2{Z}_{2}Z2​ frustrated antiferromagnets, or to particles in a multicomponent Bose gase (in which case the spin degree of freedom is attributed to hyperfine levels). Using renormalization group techniques, we establish that our impurity models, which feature an exchange interaction analogous to Kondo impurities in Fermi liquids, allow flow toward a stable strong-coupling state. Since the low-energy bosons exist around a single point in momentum space, and there is no Fermi surface, an impurity quantum phase transition occurs at intermediate coupling, separating screened and unscreened phases. This behavior is qualitatively different from previously studied spin-isotropic variants of the spin-boson model, which display stable intermediate-coupling fixed points and no screening.
By making use of the Lanczos and the density-matrix renormalization-group methods, we study the zero-temperature properties of a spin-1/2 antiferromagnetic Heisenberg chain system with a spin-1/2 magnetic impurity symmetrically coupled to its two nearest-neighbor spins. A comparison is made with the results for a magnetic impurity coupled only to the nearest-neighbor spin in the chain. The binding energy and the spin correlations are calculated. The matrix elements of the impurity spin operators are also calculated between several low-energy states. By carefully analyzing finite-size effects, we show that the dynamical structure factor of the impurity contains a \ensuremath{\delta}-function contribution at zero frequency which does not vanish in the thermodynamic limit for the case of symmetrical coupling. This indicates a partial decoupling of the impurity spin from the spins in the chain, and therefore the impurity susceptibility is predicted to show a Curie behavior. This contradicts the two-channel Kondo behavior suggested from analytic considerations.
We discuss models of interacting magnetic impurities coupled to a metallic host, which show one or more boundary quantum phase transitions where the ground-state spin changes as a function of the interimpurity couplings. The simplest example is realized by two spin-12\frac{1}{2}21​ Kondo impurities coupled to a single orbital of the host. We investigate the phase diagram and crossover behavior of this model and present numerical renormalization-group results together with general arguments showing that the singlet-doublet quantum phase transition is either of first order or of the Kosterlitz-Thouless type, depending on the symmetry of the Kondo couplings. Thus we find an exponentially small energy scale within the Kondo regime, and a two-stage Kondo effect, in a single-channel situation. Connections to other models and possible applications are discussed.