Disordered one-dimensional XYZ Heisenberg ferromagnets with substitutional impurities are studied. The substitutional spins give rise to a random distribution of the exchange couplings. By introducing a new transformation for spin operators, the XYZ Heisenberg Hamiltonian can be exactly diagonalized and expressed by Bose operators. Being restricted by the spin wave approximation, the Hamiltonian obtained is shown to be similar to the Anderson Hamiltonian for electronic systems. We have shown that the magnon localization should be destroyed at the middle of the band due to the effects of commensurability of the magnon wavelength and lattice constant. The magnon density of states and the localization length are shown to have singularities at the middle of the band irrespective of the strength of disorder. The middle of the magnon band can be reached not only by changing the magnon energy but also by varying the external magnetic field which facilitates the observation of the phenomenon.Disordered one-dimensional XYZ Heisenberg ferromagnets with substitutional impurities are studied. The substitutional spins give rise to a random distribution of the exchange couplings. By introducing a new transformation for spin operators, the XYZ Heisenberg Hamiltonian can be exactly diagonalized and expressed by Bose operators. Being restricted by the spin wave approximation, the Hamiltonian obtained is shown to be similar to the Anderson Hamiltonian for electronic systems. We have shown that the magnon localization should be destroyed at the middle of the band due to the effects of commensurability of the magnon wavelength and lattice constant. The magnon density of states and the localization length are shown to have singularities at the middle of the band irrespective of the strength of disorder. The middle of the magnon band can be reached not only by changing the magnon energy but also by varying the external magnetic field which facilitates the observation of the phenomenon.

physica status solidi (b)Feb 1, 19980 citations

Magnon delocalization in ferromagnetic chains with long-range correlated disorder

R. P. A. Lima, M. L. Lyra, Elton Malta Nascimento +1 more

We study one-magnon excitations in a random ferromagnetic Heisenberg chain with long-range correlations in the coupling constant distribution. By employing an exact diagonalization procedure, we compute the localization length of all one-magnon states within the band of allowed energies E. The random distribution of coupling constants was assumed to have a power spectrum decaying as $S(k)\ensuremath{\propto}{1/k}^{\ensuremath{\alpha}}.$ We found that for $\ensuremath{\alpha}<1,$ one-magnon excitations remain exponentially localized with the localization length $\ensuremath{\xi}$ diverging as $1/E.$ For $\ensuremath{\alpha}=1$ a faster divergence of $\ensuremath{\xi}$ is obtained. For any $\ensuremath{\alpha}>1,$ a phase of delocalized magnons emerges at the bottom of the band. We characterize the scaling behavior of the localization length on all regimes and relate it with the scaling properties of the long-range correlated exchange coupling distribution.We study one-magnon excitations in a random ferromagnetic Heisenberg chain with long-range correlations in the coupling constant distribution. By employing an exact diagonalization procedure, we compute the localization length of all one-magnon states within the band of allowed energies E. The random distribution of coupling constants was assumed to have a power spectrum decaying as $S(k)\ensuremath{\propto}{1/k}^{\ensuremath{\alpha}}.$ We found that for $\ensuremath{\alpha}<1,$ one-magnon excitations remain exponentially localized with the localization length $\ensuremath{\xi}$ diverging as $1/E.$ For $\ensuremath{\alpha}=1$ a faster divergence of $\ensuremath{\xi}$ is obtained. For any $\ensuremath{\alpha}>1,$ a phase of delocalized magnons emerges at the bottom of the band. We characterize the scaling behavior of the localization length on all regimes and relate it with the scaling properties of the long-range correlated exchange coupling distribution.

arXiv:cond-mat/0112274Physical review. B, Condensed matterFeb 13, 200220 citations

Quantum Heisenberg Spin Chains with Inversely Linear Correlated Disorder: Localization Effects and State Transfer Protocols

MARCONI SILVA SANTOS, Messias de Oliveira Sales, G. M. A. Almeida +1 more

In this work, we investigate the effects of correlated disorder on the quantum Heisenberg spin chain. The exchange couplings between adjacent spins are modeled as a disordered distribution with inverse linear correlation function controlled by a parameter 𝛾. The Cholesky decomposition method is employed to generate the spin-spin coupling that adheres to this correlation structure. By analyzing the autocorrelation function, we observe the influence of the correlation parameter 𝛾 on the decay behavior of the autocorrelation. Furthermore, we study the eigenstates of the Hamiltonian in the one-magnon subspace and calculate the density of states and the participation ratio, providing insights into the localization properties of the system. Our findings suggest that introducing correlated disorder significantly alters the physical properties of the spin chain, which could have implications for understanding disordered quantum systems and developing state transfer protocols with reasonable fidelity.In this work, we investigate the effects of correlated disorder on the quantum Heisenberg spin chain. The exchange couplings between adjacent spins are modeled as a disordered distribution with inverse linear correlation function controlled by a parameter 𝛾. The Cholesky decomposition method is employed to generate the spin-spin coupling that adheres to this correlation structure. By analyzing the autocorrelation function, we observe the influence of the correlation parameter 𝛾 on the decay behavior of the autocorrelation. Furthermore, we study the eigenstates of the Hamiltonian in the one-magnon subspace and calculate the density of states and the participation ratio, providing insights into the localization properties of the system. Our findings suggest that introducing correlated disorder significantly alters the physical properties of the spin chain, which could have implications for understanding disordered quantum systems and developing state transfer protocols with reasonable fidelity.

Anais da Academia Brasileira de CiênciasJan 1, 20250 citations

Magnetic impurities coupled to quantum antiferromagnets in one dimension

J. Igarashi, Takashi Tonegawa, Makoto Kaburagi +1 more

Magnetic impurities coupled antiferromagnetically to a one-dimensional Heisenberg model are studied by numerical diagonalization of chains of finite clusters. By calculating the binding energy and the correlation function, it is shown that a local singlet develops around each impurity. This holds true for systems with a single impurity, with two impurities, and for impurities forming a lattice. The local character of the singlet is found to be little affected by the presence of other impurity spins. A small effective interaction is found between a pair of impurity spins, which oscillates depending on impurity distances. For impurity lattices, the energy spectrum shows a gap which is found to be much smaller than the binding energy per impurity if the coupling constants are small. For larger coupling constants, it increases to the same order of magnitude as the binding energy, indicating that a local singlet is broken to create excited states. Impurity lattices with ferromagnetic couplings are also studied and their connection to the Haldane problem is discussed.Magnetic impurities coupled antiferromagnetically to a one-dimensional Heisenberg model are studied by numerical diagonalization of chains of finite clusters. By calculating the binding energy and the correlation function, it is shown that a local singlet develops around each impurity. This holds true for systems with a single impurity, with two impurities, and for impurities forming a lattice. The local character of the singlet is found to be little affected by the presence of other impurity spins. A small effective interaction is found between a pair of impurity spins, which oscillates depending on impurity distances. For impurity lattices, the energy spectrum shows a gap which is found to be much smaller than the binding energy per impurity if the coupling constants are small. For larger coupling constants, it increases to the same order of magnitude as the binding energy, indicating that a local singlet is broken to create excited states. Impurity lattices with ferromagnetic couplings are also studied and their connection to the Haldane problem is discussed.

arXiv:cond-mat/9412104Physical review. B, Condensed matterMar 1, 199554 citations

Elementary excitations of a two-dimensional Ising ferromagnet in a transverse magnetic field in the presence of impurities

Yu. G. Okladnoy, V. M. Tsukernik

The influence of a magnetic impurity on the elementary excitation spectrum of a two-dimensional Ising ferromagnet is investigated in a low transverse magnetic field. It is shown that in the case of a “ferromagnetic” impurity in a matrix of spin 1/2, from one to three local energy levels can be split off from the lower edge of the continuous spectrum of one-magnon states where the conditions for their existence impose quite strict constraints on the spin-Hamiltonian parameters. Three distinct spin configurations can be realized in the presence of an “antiferromagnetic” impurity in the crystal in the ground state. Single-magnon states of a ferromagnet are considered for those values of the spin-Hamiltonian parameters when two of them are realized. It is shown that from one to six local levels above or below the continuous spectrum band can appear, and their distance from the band edge can substantially exceed its width. Quasilocal energy levels originating within the continuous spectrum of the single-magnon states are also investigated.The influence of a magnetic impurity on the elementary excitation spectrum of a two-dimensional Ising ferromagnet is investigated in a low transverse magnetic field. It is shown that in the case of a “ferromagnetic” impurity in a matrix of spin 1/2, from one to three local energy levels can be split off from the lower edge of the continuous spectrum of one-magnon states where the conditions for their existence impose quite strict constraints on the spin-Hamiltonian parameters. Three distinct spin configurations can be realized in the presence of an “antiferromagnetic” impurity in the crystal in the ground state. Single-magnon states of a ferromagnet are considered for those values of the spin-Hamiltonian parameters when two of them are realized. It is shown that from one to six local levels above or below the continuous spectrum band can appear, and their distance from the band edge can substantially exceed its width. Quasilocal energy levels originating within the continuous spectrum of the single-magnon states are also investigated.

Soviet Journal of Low Temperature PhysicsAug 1, 19760 citations

Random-exchange and random-field x y chain for s=1/2

T. Schneider, Antonio Politi

One of the points of interest in the study of random systems is the nature of the eigenstates, i.e., exponentially localized or extended, and the density of states. To identify the disorder-induced effects, we consider the one-dimensional s=1/2 xy models with random exchange, or random field. Using the transformation to spinless fermions, the problem is reduced to a nonlinear map, providing accurate numerical estimates for the integrated density of states and the exponential localization length. The results clearly reveal: (i) appearance of disorder-induced tails in the integrated density of states at the bottom and top of the spectrum, yielding to a characteristic field dependence of magnetization and susceptibility at zero temperature; and (ii) important differences between random-exchange and random-field models. In the random-exchange case, the middle of the band is found to be extended, while in the random-field case, corresponding to the standard Anderson model, all states are exponentially localized. This difference also affects the temperature dependence of zero-field specific heat and susceptibility as T→0.One of the points of interest in the study of random systems is the nature of the eigenstates, i.e., exponentially localized or extended, and the density of states. To identify the disorder-induced effects, we consider the one-dimensional s=1/2 xy models with random exchange, or random field. Using the transformation to spinless fermions, the problem is reduced to a nonlinear map, providing accurate numerical estimates for the integrated density of states and the exponential localization length. The results clearly reveal: (i) appearance of disorder-induced tails in the integrated density of states at the bottom and top of the spectrum, yielding to a characteristic field dependence of magnetization and susceptibility at zero temperature; and (ii) important differences between random-exchange and random-field models. In the random-exchange case, the middle of the band is found to be extended, while in the random-field case, corresponding to the standard Anderson model, all states are exponentially localized. This difference also affects the temperature dependence of zero-field specific heat and susceptibility as T→0.

Journal of Applied PhysicsApr 15, 19871 citation

1/E.

For $\ensuremath{\alpha}=1$ a faster divergence of $\ensuremath{\xi}$ is obtained. For any $\ensuremath{\alpha}>1,$ a phase of delocalized magnons emerges at the bottom of the band. We characterize the scaling behavior of the localization length on all regimes and relate it with the scaling properties of the long-range correlated exchange coupling distribution.