Anais da Academia Brasileira de Ciências

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, F. A. B. F. de Moura

Published Jan 1, 2025• 0 citations

Abstract

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.

DOI: 10.1590/0001-3765202520241047

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Anais da Academia Brasileira de Ciências

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, F. A. B. F. de Moura

Published Jan 1, 2025• 0 citations

Publisher

Abstract

DOI: 10.1590/0001-3765202520241047

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From Thermalization to Multifractality: Spin-Spin Correlation in Disordered

SU(2)

-Invariant 1D Heisenberg Spin Chains

We investigate spin correlations in one-dimensional

SU(2)

-invariant Heisenberg chains with exchange disorder for spin lengths

S=1/2

and

S=1

. In the weak-disorder regime, the eigenmodes of the spin-spin correlation matrix are delocalized, consistent with ergodic behavior. Under strong disorder, the system enters a quasi-localized multifractal phase characterized by exponentially decaying, dimer-like spin correlations. Finite-size scaling of the inverse participation ratios of the correlation-matrix eigenmodes yields a correlation dimension,

D_2\approx 0.37-0.39

, confirming the stability of a multifractal regime that is distinct from both the ergodic limit (

D_2=1

) and the fully localized limit (

D_2=0

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.