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We establish a setting-atoms in optical superlattices with period 2-in which one can experimentally probe signatures of the process of local relaxation and apparent thermalization in nonequilibrium dynamics without the need of addressing single sites. This opens up a way to explore the convergence of subsystems to maximum entropy states in quenched quantum many-body systems with present technology. Remarkably, the emergence of thermal states does not follow from a coupling to an environment but is a result of the complex nonequilibrium dynamics in closed systems. We explore ways of measuring the relevant signatures of thermalization in this analogue quantum simulation of a relaxation process, exploiting the possibilities offered by optical superlattices.

In the study of relaxation processes in coherent nonequilibrium dynamics of quenched quantum systems, ultracold atoms in optical superlattices with periodicity 2 provide a very fruitful test ground. We consider the dynamics of a particular, experimentally accessible initial state prepared in a superlattice structure evolving under a Bose-Hubbard Hamiltonian in the entire range of interaction strengths, further investigating the issues raised by Cramer et al. ͓Phys. Rev. Lett. 101, 063001 ͑2008͔͒. We investigate the relaxation dynamics analytically in the noninteracting and hard-core bosonic limits, deriving explicit expressions for the dynamics of certain correlation functions, and numerically for finite interaction strengths using the time-dependent densitymatrix renormalization ͑t-DMRG͒ approach. We can identify signatures of local relaxation that can be accessed experimentally with present technology. While the global system preserves the information about the initial condition, locally the system relaxes to the state having maximum entropy respecting the constraints of the initial condition. For finite interaction strengths and finite times, the relaxation dynamics contains signatures of the relaxation dynamics of both the noninteracting and hard-core bosonic limits.

We study the mechanism of orbital-order melting observed at temperature T OO in the series of rare-earth manganites. We find that the purely electronic many-body super-exchange mechanism yields a transition temperature T KK that decreases with decreasing rare-earth radius and increases with pressure, opposite to the experimental T OO . We show that the tetragonal crystal-field splitting reduces T KK further increasing the discrepancies with experiments. This proves that super-exchange effects, although very efficient, in the light of experimentally observed trends play a minor role for the melting of orbital ordering in rare-earth manganites.

JARA High-Performance ComputingOrbital and spin ordering phenomena in strongly correlated systems are studied using the localdensity approximation + dynamical mean-field theory approach. Typically, however, such simulations are restricted to simplified models (density-density Coulomb interactions, high symmetry couplings and few-band models). In this work we implement an efficient general hybridizationexpansion continuous-time quantum Monte Carlo impurity solver (Krylov approach) which allows us to investigate orbital and spin ordering in a more realistic setting, including interactions that are often neglected (e.g., spin-flip and pair-hopping terms), enlarged basis sets (full d versus eg), low-symmetry distortions, and reaching the very low-temperature (experimental) regime. We use this solver to study ordering phenomena in a selection of exemplary low-symmetry transition-metal oxides: LaMnO3 and rare-earth manganites as well as the perovskites CaVO3 and YTiO3. We find that, in all considered cases, the minus sign problem mostly appears when off-diagonal crystal-field terms are present (and is strongly suppressed in the basis of crystal-field states), while off-diagonal terms of the hybridization function matrix are not as critical. We show that spin-flip and pair hopping terms do not affect the Kugel-Khomskii orbital-order melting transition in rare-earth manganites, or the suppression of orbital fluctuations driven by crystal field and Coulomb repulsion. For the Mott insulator YTiO3 we find a ferromagnetic transition temperature TC ∼ 50 K, in remarkably good agreement with experiments. For LaMnO3 we show that the classical t2g-spin approximation, commonly adopted for studying manganites, yields indeed an occupied eg orbital in very good agreement with that obtained for the full d 5-orbital Hubbard model, while the spin-spin eg-t2g correlation function calculated from the full d model is ∼ 0.74, very close to the value expected for aligned eg and t2g spins; the eg spectral function matrix is also well reproduced. Finally, we show that the t2g screening reduces the eg-eg Coulomb repulsion by about 10%.