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arXiv:quant-ph/0308116 · Journal of Physics A Mathematical and General

Bipartite entanglement and localization of one-particle states

Haibin Li, XiaoGuang Wang, Bambi Hu

Published Oct 21, 2004• 16 citations
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Abstract

We study bipartite entanglement in a general one-particle state, and find that the linear entropy, quantifying the bipartite entanglement, is directly connected to the participation ratio, characterizing the state localization. The more extended the state, the more entangled it is. We apply the general formalism to investigate ground-state and dynamical properties of entanglement in the one-dimensional Harper model.

DOI
10.1088/0305-4470/37/44/014

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We study thermalization in a disordered one-dimensional interacting bosonic system described by the Aubry-Andre model using full exact diagonalization. We find a broad chaotic energy window where the system's eigenstates satisfy the Eigenstate Thermalization Hypothesis (ETH), demonstrated by the smooth energy dependence of observables like entanglement entropy and local particle number, whose fluctuations decrease with system size. Dynamically, we investigate the equilibration of initial Fock states and find that thermalization is not universal. The key finding is a direct and nontrivial correlation between an initial state's delocalization in the energy eigenbasis quantified by the Participation Ratio (PR) and its subsequent equilibration. States with a high PR consistently evolve toward the microcanonical ensemble prediction, whereas those exhibiting a low PR display deviations whose magnitude inversely correlates with the PR value. This connection is quantitatively confirmed by the trace distance, providing a powerful, experimentally relevant diagnostic for predicting which initial states will reach thermal equilibrium.