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arXiv:0801.4700 · Physical Review A

Staggered magnetization and entanglement enhancement by magnetic impurities in a S=12 spin chain

Tony J. G. Apollaro, Alessandro Cuccoli, Andrea Fubini, Francesco Plastina, Paola Verrucchi

Published Jun 11, 2008• 16 citations
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Abstract

We study the effects of an impurity on the magnetic response and the entanglement properties of the infinite $S=\frac{1}{2}$ $XX$ chain in a transverse field $h$ in its quasi-long-range ordered phase, i.e., below the critical point $h=1$. We show that regardless of the sign of the exchange coupling, and for whatever value of the applied field, the impurity generates an oscillating magnetization that displays a power-law decay with the distance from the impurity itself. This effect sensibly modifies the overall magnetic behavior of the chain, as testified by the observed rounding-off of the divergence of the longitudinal susceptibility. Moreover, the emergence of the above alternating structure in the spin configuration entails a substantial change in the pairwise entanglement distribution along the chain, so that concurrences are found either enhanced (up to a factor larger than 2) or quenched, depending on the distance of the spin pair from the impurity, on its strength, and on the value of the magnetic field. Acting on such control parameters, an adiabatic manipulation of both the magnetic and entanglement properties can be performed. We find these effects robust against thermal fluctuations, and we can therefore suggest realistic setups to experimentally probe the predicted behavior.

DOI
10.1103/physreva.77.062314

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We study the effects of an impurity on the magnetic response and the entanglement properties of the infinite S=12S=\frac{1}{2}S=21​ XXXXXX chain in a transverse field hhh in its quasi-long-range ordered phase, i.e., below the critical point h=1h=1h=1. We show that regardless of the sign of the exchange coupling, and for whatever value of the applied field, the impurity generates an oscillating magnetization that displays a power-law decay with the distance from the impurity itself. This effect sensibly modifies the overall magnetic behavior of the chain, as testified by the observed rounding-off of the divergence of the longitudinal susceptibility. Moreover, the emergence of the above alternating structure in the spin configuration entails a substantial change in the pairwise entanglement distribution along the chain, so that concurrences are found either enhanced (up to a factor larger than 2) or quenched, depending on the distance of the spin pair from the impurity, on its strength, and on the value of the magnetic field. Acting on such control parameters, an adiabatic manipulation of both the magnetic and entanglement properties can be performed. We find these effects robust against thermal fluctuations, and we can therefore suggest realistic setups to experimentally probe the predicted behavior.
We study the effects of an impurity on the magnetic response and the entanglement properties of the infinite S=1/2 XX chain in a transverse field h in its quasi-long-range ordered phase, i.e., below the critical point h=1. We show that regardless of the sign of the exchange coupling, and for whatever value of the applied field, the impurity generates an oscillating magnetization that displays a power-law decay with the distance from the impurity itself. This effect sensibly modifies the overall magnetic behavior of the chain, as testified by the observed rounding-off of the divergence of the longitudinal susceptibility. Moreover, the emergence of the above alternating structure in the spin configuration entails a substantial change in the pairwise entanglement distribution along the chain, so that concurrences are found either enhanced (up to a factor larger than 2) or quenched, depending on the distance of the spin pair from the impurity, on its strength, and on the value of the magnetic field. Acting on such control parameters, an adiabatic manipulation of both the magnetic and entanglement properties can be performed. We find these effects robust against thermal fluctuations, and we can therefore suggest realistic setups to experimentally probe the predicted behavior.
We study the ground-state entanglement properties of an XX spin 1/2 chain in transverse field, in its quasi-long-ranged ordered phase, with a magnetic impurity, represented in terms of an additional transverse magnetic field located at one precise site. For such a system, we show that a control of the ground state entanglement can be achieved by acting on the impurity field. To demonstrate this possibility, we evaluate exactly the nearest neighbor and next-nearest neighbor concurrence in the presence of the impurity. It turns out that either an enhancement or a quenching of entanglement between selected spin pairs can be obtained by acting on the intensity of the impurity. For specific values of the magnetic field a spatial modulation of concurrence along the chain is also obtained.
We study the effect of anisotropy of spin-SSS impurities on an antiferromagnetic SU(2) Heisenberg chain. The magnetic impurities are assumed to have an XXZ-type anisotropic exchange with their neighboring sites. First, using density-matrix renormalization group technique, we examine spin-spin correlation function, instability of N\'eel order, and local spin susceptibility in the presence of a single spin-SSS impurity. Based on the results, we find that the types of spin-SSS impurities are classified into two groups: (i) nonmagnetic and S=1S=1S=1 impurities enhance only short-range antiferromagnetic correlation and (ii) S=12S=\frac{1}{2}S=21​ and S>1S>1S>1 impurities can, in contrast, stabilize a long-range N\'eel order in the disordered SU(2) Heisenberg chain. Then, we focus on the case of S=12S=\frac{1}{2}S=21​ impurity as a representative of (ii) and investigate the evolution of some experimentally observable quantities such as magnetization, specific heat, and magnetic susceptibility, as a function of concentration and XXZ anisotropy strength of the impurity. We confirm that the N\'eel order is induced in the bulk spin chain in the presence of finite amount of easy-axis XXZ S=12S=\frac{1}{2}S=21​ impurities. Furthermore, we recover some of the aforementioned features using cluster mean-field theory, which allows us to present results on experimentally accessible quantities at finite temperatures. Interestingly, in the presence of uniform magnetic field, the total magnetization exhibits a pseudogap behavior for low values of applied field. We also discuss the dependence of NMR spectrum on various XXZ impurities and identify that the spin state of Co impurity in SrCu0.99Co0.01O2{\mathrm{SrCu}}_{0.99}{\mathrm{Co}}_{0.01}{\mathrm{O}}_{2}SrCu0.99​Co0.01​O2​ is S=32S=\frac{3}{2}S=23​.
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.
For a three-qubit Heisenberg model in a uniform magnetic field, the pairwise thermal entanglement of any two sites is identical due to the exchange symmetry of sites. In this paper we consider the effect of a non-uniform magnetic field on the Heisenberg model, modelling a magnetic impurity on one site. Since pairwise entanglement is calculated by tracing out one of the three sites, the entanglement clearly depends on which site the impurity is located. When the impurity is located on the site which is traced out, that is, when it acts as an external field of the pair, the entanglement can be enhanced to the maximal value 1; while when the field acts on a site of the pair the corresponding concurrence can only be increased from 1/3 to 2/3.
Entanglement measures are useful tools in characterizing otherwise unknown quantum phases and indicating transitions between them. Here we examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $\ensuremath{\alpha}$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $\ensuremath{\alpha}>\frac{1}{2}$. A numerical implementation of the SDRG method yields a power-law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading-order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $\ensuremath{\alpha}$, corresponding to a critical behavior with an effective central charge c=ln(2)c=\mathrm{ln}(2)c=ln(2), independent of $\ensuremath{\alpha}$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $\ensuremath{\alpha}$. For a wide range of partition size lll, the EE fits a critical behavior with a central charge close to c=1c=1c=1, which is the same as for the clean Haldane-Shastry model with a power-law-decaying interaction with $\ensuremath{\alpha}=2$. Only for small $l\ensuremath{\ll}L$, in a range which increases with the number of spins NNN, we find deviations which are rather consistent with the strong disorder fixed point central charge c=ln(2)c=\mathrm{ln}(2)c=ln(2). Furthermore, we find using ED that the concurrence shows power-law decay, albeit with smaller power exponents than obtained by SDRG. We also present results obtained with DMRG and find agreement with ED for sufficiently small $\ensuremath{\alpha}<2$, whereas for larger $\ensuremath{\alpha}$ DMRG tends to underestimate the entanglement entropy and finds a faster decaying concurrence.