Structure of the Hilbert-space of the infinite-dimensional Hubbard model

An iterative procedure for the explicit construction of the nontrivial subspace of all symmetry-adapted configurations with non-zero weight in the ground-state of the infinite-dimensional Hubbard model is developed on the basis of a symmetrized representation of the transition operators on a sequence of Bethe-Lattices of finite depth. The relation ship between these operators and the well known mapping of the infinite-dimensional Hubbard model onto an effective impurity problem coupled to a (self-consistent) bath on non-interacting electrons is given. As an application we calculate the properties of various Hubbard stars and give estimates for the half-filled Hubbard model with up to 0.1% accuracy.Comment: accepted for publication in EJP

Validation of purdue engineering shape benchmark clusters by crowdsourcing

The effective organization of CAD data archives is central to PLM and consequently content based retrieval of 2D drawings and 3D models is often seen as a "holy grail" for the industry. Given this context, it is not surprising that the vision of a "Google for shape", which enables engineers to search databases of 3D models for components similar in shape to a query part, has motivated numerous researchers to investigate algorithms for computing geometric similarity. Measuring the effectiveness of the many approaches proposed has in turn lead to the creation of benchmark datasets against which researchers can compare the performance of their search engines. However to be useful the datasets used to measure the effectiveness of 3D retrieval algorithms must not only define a collection of models, but also provide a canonical specification of their relative similarity. Because the objective of shape retrieval algorithms is (typically) to retrieve groups of objects that humans perceive as "similar" these benchmark similarity relationships have (by definition) to be manually determined through inspection

Breakdown of the Luttinger sum-rule at the Mott-Hubbard transition in the one-dimensional t1-t2 Hubbard model

We investigate the momentum distribution function near the Mott-Hubbard transition in the one-dimensional t1-t2 Hubbard model (the zig-zag Hubbard chain), with the density-matrix renormalization-group technique. We show that for strong interactions the Mott-Hubbard transition occurs between the metallic-phase and an insulating dimerized phase with incommensurate spin excitations, suggesting a decoupling of magnetic and charge excitations not present in weak coupling. We illustrate the signatures for the Mott-Hubbard transition and the commensurate-incommensurate transition in the insulating spin-gapped state in their respective ground-state momentum distribution functions