Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0112274 · Physical review. B, Condensed matter

Magnon delocalization in ferromagnetic chains with long-range correlated disorder

R. P. A. Lima, M. L. Lyra, Elton Malta Nascimento, Antônio D. de Jesus

Published Feb 13, 2002• 20 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.65.104416

Related papers

Delocalization and spin-wave dynamics in ferromagnetic chains with long-range correlated random exchange

F. A. B. F. de Moura, Mauricio D. Coutinho-Filho, Ernesto P. Raposo +1 more

We study the one-dimensional quantum Heisenberg ferromagnet with exchange couplings exhibiting long-range correlated disorder with power spectrum proportional to ${1/k}^{\ensuremath{\alpha}},$ where k is the wave vector of the modulations on the random coupling landscape. By using the renormalization group, integration of the equations of motion, and exact diagonalization, we compute the spin-wave localization length and the mean-square displacement of the wave packet. We find that, associated with the emergence of extended spin waves in the low-energy region for \ensuremath{\alpha}>1, the wave-packet mean-square displacement changes from a long-time super diffusive behavior for \ensuremath{\alpha}1 to a long-time ballistic behavior for \ensuremath{\alpha}>1. At the vicinity of \ensuremath{\alpha}=1, the mobility edge separating the extended and localized phases is shown to scale with the degree of correlation as ${E}_{c}\ensuremath{\propto}(\ensuremath{\alpha}\ensuremath{-}{1)}^{1/3}.$

arXiv:cond-mat/0206038•Physical review. B, Condensed matter•Jul 8, 2002•60 citations

Magnon Localization in One-Dimensional Disordered XYZ Heisenberg Ferromagnets

É. P. Nakhmedov, É. P. Nakhmedov, M. Alp +2 more

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, 1998•0 citations

Excited-eigenstate entanglement properties of XX spin chains with random long-range interactions

Y. Mohdeb, Javad Vahedi, Stefan Kettemann

Quantum information theoretical measures are useful tools for characterizing quantum dynamical phases. However, employing them to study excited states of random spin systems is a challenging problem. Here, we report results for the entanglement entropy (EE) scaling of excited eigenstates of random XX antiferromagnetic spin chains with long-range (LR) interactions decaying as a power law with distance with exponent $\ensuremath{\alpha}$. To this end, we extend the real-space renormalization group technique for excited states (RSRG-X) to solve this problem with LR interactions. For comparison, we perform numerical exact diagonalization (ED) calculations. From the distribution of energy-level spacings, as obtained by ED for up to $N\ensuremath{\sim}18$ spins, we find indications of a delocalization transition at ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}1$ in the middle of the energy spectrum. With RSRG-X and ED, we show that for $\ensuremath{\alpha}>{\ensuremath{\alpha}}^{*}$ the EE of excited eigenstates retains a logarithmic divergence similar to the one observed for the ground state of the same model, while for $\ensuremath{\alpha}<{\ensuremath{\alpha}}^{*}$ EE displays an algebraic growth with the subsystem size $l, {S}_{l}\ensuremath{\sim}{l}^{\ensuremath{\beta}}$, with $0<\ensuremath{\beta}<1$. We find that ${\ensuremath{\alpha}}^{*}\ensuremath{\approx}1$ coincides with the delocalization transition ${\ensuremath{\alpha}}_{c}$ in the middle of the many-body spectrum. An interpretation of these results based on the structure of the RG rules is proposed, which is due to rainbow proliferation for very long-range interactions $\ensuremath{\alpha}\ensuremath{\ll}1$. We also investigate the effective temperature dependence of the EE, allowing us to study the half-chain EE of eigenstates at different energy densities, where we find that the crossover in EE occurs at ${\ensuremath{\alpha}}^{*}<1$.

arXiv:2201.10607•Physical review. B./Physical review. B•Sep 14, 2022•7 citations

Stationary and dynamical aspects of two-magnon states in disordered ferromagnetic chains

Elton Malta Nascimento, F. A. B. F. de Moura, M. L. Lyra

We study the nature of collective two-spin excitations in disordered $S=1∕2$ ferromagnetic chains. Using a direct diagonalization scheme, we characterize the two-magnon eigenstates by computing their spacial extent, two-point correlation and the average distance between the excited spins within the allowed energy band. We found that, due to the effective excitation interaction imposed by the exclusion rule, the low-energy two-magnon states display strong spin-spin correlations as compared to the more localized high-energy states. We further solve the time-dependent Schroedinger equation to follow the time evolution of an initially localized two-magnon state. We show that the effective one-magnon wave packet develops power-law tails with distinct exponents for the left and right tails, with the distribution function of the spin-spin distance decaying as $P(d)\ensuremath{\propto}1∕d$. We show that the average distance between the two excited spins evolves in time diffusively, while the wave-packet dispersion evolves superdiffusively.

Physical Review B•Dec 14, 2005•3 citations

Magnon Localization in One-Dimensional Disordered XYZ Heisenberg Ferromagnets

É. P. Nakhmedov, É. P. Nakhmedov, M. Alp +2 more

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, 1998•1 citation

Many-body localization transition in random quantum spin chains with long-range interactions

N. Moure, Stephan Haas, Stefan Kettemann

While there are well-established methods to study delocalization transitions of single particles in random systems, it remains a challenging problem how to characterize many-body delocalization transitions. Here, we use a generalized real-space renormalization group technique to study the anisotropic Heisenberg model with long-range interactions, decaying with a power α , which are generated by placing spins at random positions along the chain. This method permits a large-scale finite-size scaling analysis. We examine the full distribution function of the excitation energy gap from the ground state and observe a crossover with decreasing α . At α c the full distribution coincides with a critical function. Thereby, we find strong evidence for the existence of a many-body localization transition in disordered antiferromagnetic spin chains with long-range interactions.

arXiv:1408.2068•Europhysics Letters (EPL)•Jul 1, 2015•16 citations
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∝1/k\ensuremathα.S(k)\ensuremath{\propto}{1/k}^{\ensuremath{\alpha}}.S(k)\ensuremath∝1/k\ensuremathα. We found that for \ensuremathα<1,\ensuremath{\alpha}<1,\ensuremathα<1, one-magnon excitations remain exponentially localized with the localization length \ensuremathξ\ensuremath{\xi}\ensuremathξ diverging as 1/E.1/E.1/E. For \ensuremathα=1\ensuremath{\alpha}=1\ensuremathα=1 a faster divergence of \ensuremathξ\ensuremath{\xi}\ensuremathξ is obtained. For any \ensuremathα>1,\ensuremath{\alpha}>1,\ensuremathα>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 the one-dimensional quantum Heisenberg ferromagnet with exchange couplings exhibiting long-range correlated disorder with power spectrum proportional to ${1/k}^{\ensuremath{\alpha}},$ where k is the wave vector of the modulations on the random coupling landscape. By using the renormalization group, integration of the equations of motion, and exact diagonalization, we compute the spin-wave localization length and the mean-square displacement of the wave packet. We find that, associated with the emergence of extended spin waves in the low-energy region for \ensuremath{\alpha}>1, the wave-packet mean-square displacement changes from a long-time super diffusive behavior for \ensuremath{\alpha}1 to a long-time ballistic behavior for \ensuremath{\alpha}>1. At the vicinity of \ensuremath{\alpha}=1, the mobility edge separating the extended and localized phases is shown to scale with the degree of correlation as ${E}_{c}\ensuremath{\propto}(\ensuremath{\alpha}\ensuremath{-}{1)}^{1/3}.$
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.
Quantum information theoretical measures are useful tools for characterizing quantum dynamical phases. However, employing them to study excited states of random spin systems is a challenging problem. Here, we report results for the entanglement entropy (EE) scaling of excited eigenstates of random XX antiferromagnetic spin chains with long-range (LR) interactions decaying as a power law with distance with exponent $\ensuremath{\alpha}$. To this end, we extend the real-space renormalization group technique for excited states (RSRG-X) to solve this problem with LR interactions. For comparison, we perform numerical exact diagonalization (ED) calculations. From the distribution of energy-level spacings, as obtained by ED for up to $N\ensuremath{\sim}18$ spins, we find indications of a delocalization transition at ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}1$ in the middle of the energy spectrum. With RSRG-X and ED, we show that for $\ensuremath{\alpha}>{\ensuremath{\alpha}}^{*}$ the EE of excited eigenstates retains a logarithmic divergence similar to the one observed for the ground state of the same model, while for $\ensuremath{\alpha}<{\ensuremath{\alpha}}^{*}$ EE displays an algebraic growth with the subsystem size $l, {S}_{l}\ensuremath{\sim}{l}^{\ensuremath{\beta}}$, with $0<\ensuremath{\beta}<1$. We find that ${\ensuremath{\alpha}}^{*}\ensuremath{\approx}1$ coincides with the delocalization transition ${\ensuremath{\alpha}}_{c}$ in the middle of the many-body spectrum. An interpretation of these results based on the structure of the RG rules is proposed, which is due to rainbow proliferation for very long-range interactions $\ensuremath{\alpha}\ensuremath{\ll}1$. We also investigate the effective temperature dependence of the EE, allowing us to study the half-chain EE of eigenstates at different energy densities, where we find that the crossover in EE occurs at ${\ensuremath{\alpha}}^{*}<1$.
We study the nature of collective two-spin excitations in disordered S=1∕2S=1∕2S=1∕2 ferromagnetic chains. Using a direct diagonalization scheme, we characterize the two-magnon eigenstates by computing their spacial extent, two-point correlation and the average distance between the excited spins within the allowed energy band. We found that, due to the effective excitation interaction imposed by the exclusion rule, the low-energy two-magnon states display strong spin-spin correlations as compared to the more localized high-energy states. We further solve the time-dependent Schroedinger equation to follow the time evolution of an initially localized two-magnon state. We show that the effective one-magnon wave packet develops power-law tails with distinct exponents for the left and right tails, with the distribution function of the spin-spin distance decaying as $P(d)\ensuremath{\propto}1∕d$. We show that the average distance between the two excited spins evolves in time diffusively, while the wave-packet dispersion evolves superdiffusively.
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.
While there are well-established methods to study delocalization transitions of single particles in random systems, it remains a challenging problem how to characterize many-body delocalization transitions. Here, we use a generalized real-space renormalization group technique to study the anisotropic Heisenberg model with long-range interactions, decaying with a power α , which are generated by placing spins at random positions along the chain. This method permits a large-scale finite-size scaling analysis. We examine the full distribution function of the excitation energy gap from the ground state and observe a crossover with decreasing α . At α c the full distribution coincides with a critical function. Thereby, we find strong evidence for the existence of a many-body localization transition in disordered antiferromagnetic spin chains with long-range interactions.