Locating the quantum critical point of the Bose-Hubbard model through singularities of simple observables

We show that the critical point of the two-dimensional Bose-Hubbard model can be easily found through studies of either on-site atom number fluctuations or the nearest-neighbor two-point correlation function (the expectation value of the tunnelling operator). Our strategy to locate the critical point is based on the observation that the derivatives of these observables with respect to the parameter that drives the superfluid-Mott insulator transition are singular at the critical point in the thermodynamic limit. Performing the quantum Monte Carlo simulations of the two-dimensional Bose-Hubbard model, we show that this technique leads to the accurate determination of the position of its critical point. Our results can be easily extended to the three-dimensional Bose-Hubbard model and different Hubbard-like models. They provide a simple experimentally-relevant way of locating critical points in various cold atomic lattice systems.Comment: 8 pages, rewritten title, abstract & introductio

Poisson-to-Wigner crossover transition in the nearest-neighbor spacing statistics of random points on fractals

We show that the nearest-neighbor spacing distribution for a model that consists of random points uniformly distributed on a self-similar fractal is the Brody distribution of random matrix theory. In the usual context of Hamiltonian systems, the Brody parameter does not have a definite physical meaning, but in the model considered here, the Brody parameter is actually the fractal dimension. Exploiting this result, we introduce a new model for a crossover transition between Poisson and Wigner statistics: random points on a continuous family of self-similar curves with fractal dimension between 1 and 2. The implications to quantum chaos are discussed, and a connection to conservative classical chaos is introduced.Comment: Low-resolution figure is included here. Full resolution image available (upon request) from the author

HD-Index: Pushing the Scalability-Accuracy Boundary for Approximate kNN Search in High-Dimensional Spaces

Nearest neighbor searching of large databases in high-dimensional spaces is inherently difficult due to the curse of dimensionality. A flavor of approximation is, therefore, necessary to practically solve the problem of nearest neighbor search. In this paper, we propose a novel yet simple indexing scheme, HD-Index, to solve the problem of approximate k-nearest neighbor queries in massive high-dimensional databases. HD-Index consists of a set of novel hierarchical structures called RDB-trees built on Hilbert keys of database objects. The leaves of the RDB-trees store distances of database objects to reference objects, thereby allowing efficient pruning using distance filters. In addition to triangular inequality, we also use Ptolemaic inequality to produce better lower bounds. Experiments on massive (up to billion scale) high-dimensional (up to 1000+) datasets show that HD-Index is effective, efficient, and scalable.Comment: PVLDB 11(8):906-919, 201

Exchange couplings for Mn ions in CdTe: validity of spin models for dilute magnetic II-VI semiconductors

We employ density-functional theory (DFT) in the generalized gradient approximation (GGA) and its extensions GGA+$U$ and GGA+Gutzwiller to calculate the magnetic exchange couplings between pairs of Mn ions substituting Cd in a CdTe crystal at very small doping. DFT(GGA) overestimates the exchange couplings by a factor of three because it underestimates the charge-transfer gap in Mn-doped II-VI semiconductors. Fixing the nearest-neighbor coupling $J_1$ to its experimental value in GGA+$U$, in GGA+Gutzwiller, or by a simple scaling of the DFT(GGA) results provides acceptable values for the exchange couplings at 2nd, 3rd, and 4th neighbor distances in Cd(Mn)Te, Zn(Mn)Te, Zn(Mn)Se, and Zn(Mn)S. In particular, we recover the experimentally observed relation $J_4>J_2,J_3$. The filling of the Mn 3$d$-shell is not integer which puts the underlying Heisenberg description into question. However, using a few-ion toy model the picture of a slightly extended local moment emerges so that an integer $3d$-shell filling is not a prerequisite for equidistant magnetization plateaus, as seen in experiment.Comment: 12 pages, 10 figure

Gutzwiller study of extended Hubbard models with fixed boson densities

We studied all possible ground states, including supersolid (SS) phases and phase separations of hard-core- and soft-core-extended Bose--Hubbard models with fixed boson densities by using the Gutzwiller variational wave function and the linear programming method. We found that the phase diagram of the soft-core model depends strongly on its transfer integral. Furthermore, for a large transfer integral, we showed that an SS phase can be the ground state even below or at half filling against the phase separation. We also found that the density difference between nearest-neighbor sites, which indicates the density order of the SS phase, depends strongly on the boson density and transfer integral.Comment: 14 pages, 14 figures, to be published in Phys. Rev.

Structure of plastically compacting granular packings

The developing structure in systems of compacting ductile grains were studied experimentally in two and three dimensions. In both dimensions, the peaks of the radial distribution function were reduced, broadened, and shifted compared with those observed in hard disk- and sphere systems. The geometrical three--grain configurations contributing to the second peak in the radial distribution function showed few but interesting differences between the initial and final stages of the two dimensional compaction. The evolution of the average coordination number as function of packing fraction is compared with other experimental and numerical results from the literature. We conclude that compaction history is important for the evolution of the structure of compacting granular systems.Comment: 12 pages, 12 figure

A tetrahedral space-filling curve for non-conforming adaptive meshes

We introduce a space-filling curve for triangular and tetrahedral red-refinement that can be computed using bitwise interleaving operations similar to the well-known Z-order or Morton curve for cubical meshes. To store sufficient information for random access, we define a low-memory encoding using 10 bytes per triangle and 14 bytes per tetrahedron. We present algorithms that compute the parent, children, and face-neighbors of a mesh element in constant time, as well as the next and previous element in the space-filling curve and whether a given element is on the boundary of the root simplex or not. Our presentation concludes with a scalability demonstration that creates and adapts selected meshes on a large distributed-memory system.Comment: 33 pages, 12 figures, 8 table

Exact ground states and correlation functions of chain and ladder models of interacting hardcore bosons or spinless fermions

By removing one empty site between two occupied sites, we map the ground states of chains of hardcore bosons and spinless fermions with infinite nearest-neighbor repulsion to ground states of chains of hardcore bosons and spinless fermions without nearest-neighbor repulsion respectively, and ultimately in terms of the one-dimensional Fermi sea. We then introduce the intervening-particle expansion, where we write correlation functions in such ground states as a systematic sum over conditional expectations, each of which can be ultimately mapped to a one-dimensional Fermi-sea expectation. Various ground-state correlation functions are calculated for the bosonic and fermionic chains with infinite nearest-neighbor repulsion, as well as for a ladder model of spinless fermions with infinite nearest-neighbor repulsion and correlated hopping in three limiting cases. We find that the decay of these correlation functions are governed by surprising power-law exponents.Comment: 20 pages, 18 figures, RevTeX4 clas