We consider long-range correlated disorder and mutual interacting particles according to a dipole-dipole coupling as modifications to the one-dimensional Anderson model. Technically, we rely on the numerical exact diagonalization of the system's Hamilitonian. From the perspective of different localization measures, we confirm and extend the picture of the emergence of delocalized states with increasing correlations. Besides these studies, a definition for multiparticle localization is proposed. In the case of two interacting bosons, we observe a sensitivity of localization with respect to the range of the particle-particle interaction and insensitivity to the coupling's sign, which should stimulate new theoretical approaches and experimental investigations with, e.g., dipolar cold quantum gases.
We consider long-range correlated disorder and mutual interacting particles according to a dipole-dipole coupling as modifications to the one-dimensional Anderson model. Technically, we rely on the numerical exact diagonalization of the system's Hamilitonian. From the perspective of different localization measures, we confirm and extend the picture of the emergence of delocalized states with increasing correlations. Besides these studies, a definition for multiparticle localization is proposed. In the case of two interacting bosons, we observe a sensitivity of localization with respect to the range of the particle-particle interaction and insensitivity to the coupling's sign, which should stimulate new theoretical approaches and experimental investigations with, e.g., dipolar cold quantum gases.
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.
We introduce a two-dimensional short-range correlated disorder that is the natural generalization of the well-known one-dimensional dual random dimer model [D. H. Dunlap et al., Phys. Rev. Lett. 65, 88 (1990)]. We demonstrate that, as in one dimension, this model induces a localization-delocalization transition in the single-particle spectrum. Moreover we show that the effect of such a disorder on a weakly interacting boson gas is to enhance the condensate spatial homogeneity and delocalization and to increase the condensate fraction around an effective resonance of the two-dimensional dual dimers. This study proves that short-range correlations of a disordered potential can enhance the quantum coherence of a weakly interacting many-body system.
We show that the crossover from the weak interaction limit towards the strong interaction limit may be accompanied by a delocalization effect in one dimensional disordered quantum models. The spin degrees of freedom are frozen and the spatial wave functions remain symmetric or antisymmetric when the strength U of a short range interaction is varied. The study concerns the excited states for two interacting particles and the ground state for a finite density of carriers. First, for two particles in a chain of length L, we establish a duality transformation mapping the behavior at weak U onto the behavior at strong U. For intermediate U, the mixing of the one body states and the interaction induced delocalization effect are maximum. Furthermore, if L ≈︂ L1 (the one particle localization length), the system becomes weakly chaotic with critical spectral statistics. This weak chaos is related to the multifractality of the interaction matrix. For two particles starting close to each other, localization is reached in two steps. Before the time t1 necessary to propagate over L1 , U de-favors the propagation. On the contrary, U favors a very slow delocalization after t1 , characterized by a log(t) spreading of the center of mass. Similarly, the curvatures of the energy levels with respect to an enclosed magnetic flux decrease as a function of U for L < L1 and increase for L > L1 . The changes of the curvatures can be described by a conductance-like single scaling parameter. Second, using the density renormalization group algorithm, we have studied the ground state energy of a finite density of spinless fermions and its change under twisted boundary conditions. For a large disorder, a charge reorganization is induced by the interaction: When the system becomes instable between the inhomogeneous configuration driven by the random potential (Anderson insulator) and the homogeneous one driven by repulsive interactions (Mott insulator), the ground state sensitivity can be enhanced by orders of magnitude. In contrast, no enhancement occurs at weaker disorder, when there are many particles on a scale L1.
We consider a two-parameter one-dimensional Hamiltonian with uncorrelated diagonal disorder and nonrandom long-range intersite interaction ${J}_{mn}=J∕{\ensuremath{\mid}m\ensuremath{-}n\ensuremath{\mid}}^{\ensuremath{\mu}}$. The model is critical at $1<\ensuremath{\mu}<3∕2$ and reveals the localization-delocalization transition with respect to the disorder magnitude. To detect the transition we analyze level and wave function statistics. It is demonstrated also that in the marginal case $(\ensuremath{\mu}=3∕2)$ all states are localized.
A different type of system with coupled ordered-disordered chains has given rise to considerable interest recently, as it has a variety of applications in nanostructures and biological systems such as DNA molecules. We investigate the localization/delocalization of coupled one-dimensional systems composed of one disordered chain (chain I) and another ordered chain (chain II), focusing on the interplay among the disorder, correlation, and interchain coupling. We find that for systems where chain I exhibits uncorrelated disorder, charge transport in chain I (II) is enhanced (suppressed), as the disorder in chain I leads to the localization of all states in both chains. However, for chain I with hopping amplitude t1 and long-range correlated disorder (with power-law spectral density and disorder strength W), we find there is a localization/delocalization transition for the case $W\ensuremath{\le}4{t}_{1}$, induced by interchain coupling. For W>4t1, we find there is a quantum-phase transition at finite interchain coupling Vc: The interchain coupling induces appearance of two channels of extended states for V>Vc while there is only one channel of extended states for V<Vc.
Abstract We show that the crossover from the weak interaction limit towards the strong interaction limit may be accompanied by a delocalization effect in one dimensional disordered quantum models. The spin degrees of freedom are frozen and the spatial wave functions remain symmetric or antisymmetric when the strength U of a short range interaction is varied. The study concerns the excited states for two interacting particles and the ground state for a finite density of carriers. First, for two particles in a chain of length L , we establish a duality transformation mapping the behavior at weak U onto the behavior at strong U . For intermediate U , the mixing of the one body states and the interaction induced delocalization effect are maximum. Furthermore, if L ≈︂ L 1 (the one particle localization length), the system becomes weakly chaotic with critical spectral statistics. This weak chaos is related to the multifractality of the interaction matrix. For two particles starting close to each other, localization is reached in two steps. Before the time t 1 necessary to propagate over L 1 , U de‐favors the propagation. On the contrary, U favors a very slow delocalization after t 1 , characterized by a log( t ) spreading of the center of mass. Similarly, the curvatures of the energy levels with respect to an enclosed magnetic flux decrease as a function of U for L < L 1 and increase for L > L 1 . The changes of the curvatures can be described by a conductance‐like single scaling parameter. Second, using the density renormalization group algorithm, we have studied the ground state energy of a finite density of spinless fermions and its change under twisted boundary conditions. For a large disorder, a charge reorganization is induced by the interaction: When the system becomes instable between the inhomogeneous configuration driven by the random potential (Anderson insulator) and the homogeneous one driven by repulsive interactions (Mott insulator), the ground state sensitivity can be enhanced by orders of magnitude. In contrast, no enhancement occurs at weaker disorder, when there are many particles on a scale L 1 .