Abstract
We consider a one-dimensional (1D) quantum many-body system and investigate how the interplay between interaction and on-site disorder affects spatial localization and quantum correlations. The hopping amplitude is kept constant. To measure localization, we use the number of principal components (NPC), which quantifies the spreading of the system eigenstates over vectors of a given basis set. Quantum correlations are determined by a global entanglement measure Q, which quantifies the degree of entanglement of multipartite pure states. Our studies apply analogously to a 1D system of interacting spinless fermions, hard-core bosons, or yet to an XXZ Heisenberg spin-1/2 chain. Disorder is characterized by both uncorrelated and long-range correlated random on-site energies. Dilute and half-filled chains are analyzed. In half-filled clean chains, delocalization is maximum when the particles do not interact, whereas multi-partite entanglement is largest when they do. In the presence of uncorrelated disorder, NPC and Q show a nontrivial behavior with interaction, peaking in the chaotic region. The inclusion of correlated disorder may further extend two-particle states, but the effect decreases with the number of particles and the strength of their interactions. In half-filled chains with large interaction, correlated disorder may even enhance localization.
Highlights
Disorder may significantly affect the properties of physical systems
Spatial localization of one-particle states (Anderson localization), for example, is due to uncorrelated random disorder [1, 2, 3, 4]; whereas short range [5, 6, 7] and long range correlated [8, 9] disorder have been associated with the appearance of delocalized states
We study the level of delocalization, determined by the number of principal components NPC, and the amount of multi-partite entanglement, quantified by a global entanglement measure Q, of all eigenvectors of the system
Summary
Disorder may significantly affect the properties of physical systems. Spatial localization of one-particle states (Anderson localization), for example, is due to uncorrelated random disorder [1, 2, 3, 4]; whereas short range [5, 6, 7] and long range correlated [8, 9] disorder have been associated with the appearance of delocalized states. A recent experiment [10] shows that long-range correlated disorder may either suppress or enhance localization. This scenario becomes yet more complex when two or more particles are considered and the effects of interactions are taken into account. Correlated disorder may appear in real systems [31] and may be engineered The latter includes the introduction of scatterers [10] or speckles [32] in a one-dimensional waveguide or yet the individual tuning of on-site energies via local fields [33, 34, 35]. In contrast to the extensively studied Hubbard model, where interaction occurs between particles in the same site, we consider interaction between particles in neighboring sites Both dilute and half-filled chains are analyzed.
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