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

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.