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arXiv:1109.3449 · Physical Review A

Proposed signature of Anderson localization and correlation-induced delocalization in an N -leg optical lattice

Tigran Sedrakyan, J. P. Kestner, S. Das Sarma

Published Nov 17, 2011• 18 citations
arXivHTMLPDF

Abstract

We propose a realization of the one-dimensional random dimer model and certain $N$-leg generalizations using cold atoms in an optical lattice. We show that these models exhibit multiple delocalization energies that depend strongly on the symmetry properties of the corresponding Hamiltonian, and we provide analytical and numerical results for the localization length as a function of energy. We demonstrate that the $N$-leg systems possess similarities with their one-dimensional ancestors but are demonstrably distinct. The existence of critical delocalization energies leads to dips in the momentum distribution that serve as a clear signal of the localization-delocalization transition. These momentum distributions are different for models with different group symmetries and are identical for those with the same symmetry.

DOI
10.1103/physreva.84.053621

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We propose a realization of the one-dimensional random dimer model and certain NNN-leg generalizations using cold atoms in an optical lattice. We show that these models exhibit multiple delocalization energies that depend strongly on the symmetry properties of the corresponding Hamiltonian, and we provide analytical and numerical results for the localization length as a function of energy. We demonstrate that the NNN-leg systems possess similarities with their one-dimensional ancestors but are demonstrably distinct. The existence of critical delocalization energies leads to dips in the momentum distribution that serve as a clear signal of the localization-delocalization transition. These momentum distributions are different for models with different group symmetries and are identical for those with the same symmetry.
A mixture of two fermionic species with different masses is studied in an optical lattice. The heavy fermions are subject only to thermal fluctuations, the light fermions also to quantum fluctuations. We derive the Ising-like distribution for the heavy atoms and study the localization properties of the light fermions numerically by a transfer-matrix method. In a two-dimensional system one-parameter scaling of the localization length is found with a transition from delocalized states at low temperatures to localized states at high temperature. The critical exponent of the localization length is ν≈0.88.
We study bosonic atoms in small optical lattices by exact diagonalization and observe a striking similarity to the superfluid to Mott insulator transition in macroscopic systems. The momentum distribution, the formation of an energy gap, and the pair correlation function show only a weak size dependence. For noncommensurate filling we reveal in deep lattices a mixture of localized and delocalized particles, which is sensitive to lattice imperfections. Breaking the lattice symmetry causes a Bose-glass-like behavior. We discuss the nature of excited states and orbital effects by using an exact diagonalization technique that includes higher bands.
We investigate the existence of quantum quasi-phase-transitions for an ensemble of ultracold bosons in a one-dimensional optical lattice performing exact diagonalizations of the Bose-Hubbard Hamiltonian. When an external parabolic potential is added to the system quasi-phase-transitions are induced by the competition of on-site mean-field energy, hopping energy, and energy offset among lattice sites due to the external potential and lead to the coexistence of regions of particle localization and delocalization in the lattice. We clarify the microscopic mechanisms responsible for these quasi-phase-transitions as a function of the depth of the external potential when the on-site mean-field energy is large compared to the hopping energy. In particular, we show that a model Hamiltonian involving a few Fock states can describe the behavior of energy gap, mean particle numbers per site, and number fluctuations per site almost quantitatively. The role of symmetry on the gap as a function of the depth of the external trapping potential is elucidated. We discuss possible experimental signatures of quasi-phase-transitions studying the single-particle density matrix and explain microscopically the occurrence of local maxima in the momentum distribution. The role of a thermal population of the excited states on the momentum distribution is discussed.
Many-body localization for a system of bosons trapped in a one-dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose–Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.
Many-body localization (MBL) in a one-dimensional Fermi Hubbard model with random on-site interactions is studied. While for this model all single-particle states are trivially delocalized, it is shown that for sufficiently strong disordered interactions the model is many-body localized. It is therefore argued that MBL does not necessarily rely on localization of the single-particle spectrum. This model provides a convenient platform to study pure MBL phenomenology, since Anderson localization in this model does not exist. By examining various forms of the interaction term, a dramatic effect of symmetries on charge transport is demonstrated. A possible realization in a cold atom experiment is proposed.
The interplay between disorder and interactions in quantum systems is a long-standing topic of condensed matter physics. We study the fate of a two-component one-dimensional mixture of cold atoms in the presence of a weak random potential. We show how disorder-induced localization of one species can influence the localization of the other species through interactions and identity three distinct phases: a delocalized phase described by a two-component Luttinger liquid, a hybrid phase where only one species is localized and a fully localized phase where both components of the mixture are localized. The latter phase is characterized by two nested localization length scales. We present the possible signatures of these phases in various observables such as the structure factors (related to Bragg scattering experiments) and the momentum distributions observed in time-of-flight experiments.