Engineering Local optimality in Quantum Monte Carlo algorithms

Quantum Monte Carlo algorithms based on a world-line representation such as the worm algorithm and the directed loop algorithm are among the most powerful numerical techniques for the simulation of non-frustrated spin models and of bosonic models. Both algorithms work in the grand-canonical ensemble and have a non-zero winding number. However, they retain a lot of intrinsic degrees of freedom which can be used to optimize the algorithm. We let us guide by the rigorous statements on the globally optimal form of Markov chain Monte Carlo simulations in order to devise a locally optimal formulation of the worm algorithm while incorporating ideas from the directed loop algorithm. We provide numerical examples for the soft-core Bose-Hubbard model and various spin-S models.Comment: replaced with published versio

Condensate fragmentation as a sensitive measure of the quantum many-body behavior of bosons with long-range interactions

The occupation of more than one single-particle state and hence the emergence of fragmentation is a many-body phenomenon universal to systems of spatially confined interacting bosons. In the present study, we investigate the effect of the range of the interparticle interactions on the fragmentation degree of one- and two-dimensional systems. We solve the full many-body Schr\"odinger equation of the system using the recursive implementation of the multiconfigurational time-dependent Hartree for bosons method, R-MCTDHB. The dependence of the degree of fragmentation on dimensionality, particle number, areal or line density and interaction strength is assessed. It is found that for contact interactions, the fragmentation is essentially density independent in two dimensions. However, fragmentation increasingly depends on density the more long-ranged the interactions become. The degree of fragmentation is increasing, keeping the particle number $N$ fixed, when the density is decreasing as expected in one spatial dimension. We demonstrate that this remains, nontrivially, true also for long-range interactions in two spatial dimensions. We, finally, find that within our fully self-consistent approach, the fragmentation degree, to a good approximation, decreases universally as $N^{-1/2}$ when only $N$ is varied.Comment: 8 pages of RevTex4-1, 5 figure

Phase diagram of Bose-Fermi mixtures in one-dimensional optical lattices

The ground state phase diagram of the one-dimensional Bose-Fermi Hubbard model is studied in the canonical ensemble using a quantum Monte Carlo method. We focus on the case where both species have half filling in order to maximize the pairing correlations between the bosons and the fermions. In case of equal hopping we distinguish between phase separation, a Luttinger liquid phase and a phase characterized by strong singlet pairing between the species. True long-range density waves exist with unequal hopping amplitudes.Comment: 5 pages, 5 figures, replaced with published versio

Vacancy supersolid of hard-core bosons on the square lattice

The ground state of hard-core bosons on the square lattice with nearest and next-nearest neighbor repulsion is studied by Quantum Monte Carlo simulations. A supersolid phase with vacancy condensation and 'star' diagonal ordering is found for filling less than a quarter. At fillings above one quarter, a supersolid phase exists between the star and the stripe crystal at half-filling. No supersolid phase occurs above quarter-filling, if the ground state at half-filling is either a checkerboard crystal or a superfluid. No commensurate supersolid phase is observed.Comment: Replaced with published versio

Phases, many-body entropy measures and coherence of interacting bosons in optical lattices

Already a few bosons with contact interparticle interactions in small optical lattices feature a variety of quantum phases: superfluid, Mott-insulator and fermionized Tonks gases can be probed in such systems. To detect these phases -- pivotal for both experiment and theory -- as well as their many-body properties we analyze several distinct measures for the one-body and many-body Shannon information entropies. We exemplify the connection of these entropies with spatial correlations in the many-body state by contrasting them to the Glauber normalized correlation functions. To obtain the ground-state for lattices with commensurate filling (i.e. an integer number of particles per site) for the full range of repulsive interparticle interactions we utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) in order to solve the many-boson Schr\"odinger equation. We demonstrate that all emergent phases -- the superfluid, the Mott insulator, and the fermionized gas can be characterized equivalently by our many-body entropy measures and by Glauber's normalized correlation functions. In contrast to our many-body entropy measures, single-particle entropy cannot capture these transitions.Comment: 11 pages, 7 figures, software available at http://ultracold.or

Dynamical mean field solution of the Bose-Hubbard model

We present the effective action and self-consistency equations for the bosonic dynamical mean field (B-DMFT) approximation to the bosonic Hubbard model and show that it provides remarkably accurate phase diagrams and correlation functions. To solve the bosonic dynamical mean field equations we use a continuous-time Monte Carlo method for bosonic impurity models based on a diagrammatic expansion in the hybridization and condensate coupling. This method is readily generalized to bosonic mixtures, spinful bosons, and Bose-Fermi mixtures.Comment: 10 pages, 3 figures. includes supplementary materia

Impact of chromophores on colour appearance in a computational skin model

Early diagnosis of skin cancer offers the patient more favorable treatment options. Color fidelity of skin images is a major concern for dermatologists as adoption of digital dermatoscopes is increasing rapidly. Accurate color depiction of the lesion and surrounding skin are vital in diagnostic evaluation of a lesion. We previously introduced VCT-Derma, a pipeline for dermatological Virtual Clinical Trials (VCTs) including detailed and flexible models of human skin and lesions, which represent the patient in the entire dermatoscopy-based diagnostic process. However, those initial models of skin and lesions did not properly account for tissue colors. Our new skin model accounts for tissue color appearance by incorporating chromophores (e.g., melanin, blood) into the tissue model, and simulating the optical properties of the various skin layers. The physical properties of the skin and lesion were selected from clinically plausible values. The model and simulated dermatoscope images were created in open modelling software, assuming a linear camera model. We have assumed ambient white lighting, with a 6mm distance to the camera. Our model of color appearance was characterised by comparing the brightness of the lesion to its depth. The brightness of the lesion is compared through the variability of the mean gray values of a cropped region around the lesion. We compare two skin models, one without extensive chromophore content and one with. Our preliminary evaluation of increasing chromophore content shows promise based on the results presented here. Further refinement and validation of the model is ongoing

Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.Comment: 4+epsilon pages, 4 figure

Electromagnetic and Gravitational Invariants

The curvature invariants have been subject of recent interest in the context of the experimental detection of the gravitomagnetic field, namely due to the debate concerning the notions of "extrinsic" and "intrinsic" gravitomagnetism. In this work we explore the physical meaning of the curvature invariants, dissecting their relationship with the gravitomagnetic effects