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International Journal of Modern Physics C

Influence of the disorder correlation length on localization and quantum state transference in tight-binding channels

Jefferson D. S. Silva, G. M. A. Almeida, M. L. Lyra, F. A. B. F. de Moura

Published Apr 5, 2024• 0 citations
Publisher

Abstract

We investigate in detail the transference of quantum states in a disordered channel. We consider a one-dimensional tight-binding model consisting of a source S connected to a receiver R throughout a disordered channel. The disorder distribution contains a single tunable spatial correlation length. We demonstrate that the disorder correlation length plays a relevant role within the localization properties of the channel. The hopping parameter between the sites S and R and the channel are also adjustable parameters. We investigate the possibility of transference of quantum states along this quantum channel model and describe the optimal conditions for the occurrence of a high fidelity process.

DOI
10.1142/s0129183124501444

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Abstract We investigate two one-dimensional tight-binding models with disorder that have extended states at zero energy. We use exact and partial diagonalisation of the Hamiltonian to obtain the eigenmodes and the associated participation ratios, and the transfer-matrix method to determine the localisation length. The first model has no on-site disorder, but random couplings. While the participation ratio remains finite at zero energy, the localisation length diverges logarithmically as the energy goes to zero. We provide an intuitive derivation of this logarithmic divergence based on the weak coupling of the two sublattices. The second model has a conserved quantity as the row sums of the Hamiltonian are zero. This model can be represented as a harmonic chain with random couplings, or as a diffusion model on a lattice with random links. We find, in agreement with existing analytical calculations, that the number of system-spanning eigenmodes increases proportionally to the square root of the system size, and we related this power law to other power laws that characterise the scaling behaviour of the eigenmodes, the participation ratio, the localisation length, and their dependence on energy and system size. When disorder is so strong that the smallest hopping terms can be arbitrarily close to zero, all these power laws change, and we show a crossover between the two scaling regimes. All these results are explained by intuitive arguments based on scaling.
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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.