The Bose-Hubbard model on a triangular lattice with diamond ring-exchange

Ring-exchange interactions have been proposed as a possible mechanism for a Bose-liquid phase at zero temperature, a phase that is compressible with no superfluidity. Using the Stochastic Green Function algorithm (SGF), we study the effect of these interactions for bosons on a two-dimensional triangular lattice. We show that the supersolid phase, that is known to exist in the ground state for a wide range of densities, is rapidly destroyed as the ring-exchange interactions are turned on. We establish the ground-state phase diagram of the system, which is characterized by the absence of the expected Bose-liquid phase.Comment: 6 pages, 10 figure

Local Density of the Bose Glass Phase

We study the Bose-Hubbard model in the presence of on-site disorder in the canonical ensemble and conclude that the local density of the Bose glass phase behaves differently at incommensurate filling than it does at commensurate one. Scaling of the superfluid density at incommensurate filling of $\rho=1.1$ and on-site interaction $U=80t$ predicts a superfluid-Bose glass transition at disorder strength of $\Delta_c \approx 30t$. At this filling the local density distribution shows skew behavior with increasing disorder strength. Multifractal analysis also suggests a multifractal behavior resembling that of the Anderson localization. Percolation analysis points to a phase transition of percolating non-integer filled sites around the same value of disorder. Our findings support the scenario of percolating superfluid clusters enhancing Anderson localization near the superfluid-Bose glass transition. On the other hand, the behavior of the commensurate filled system is rather different. Close to the tip of the Mott lobe ($\rho=1, U=22t$) we find a Mott insulator-Bose glass transition at disorder strength of $\Delta_c \approx 16t$. An analysis of the local density distribution shows Gaussian like behavior for a wide range of disorders above and below the transition.Comment: 12 pages, 14 figure

Using off-diagonal confinement as a cooling method

In a recent letter [Phys. Rev. Lett. 104, 167201 (2010)] we proposed a new confining method for ultracold atoms on optical lattices, based on off-diagonal confinement (ODC). This method was shown to have distinct advantages over the conventional diagonal confinement (DC) that makes use of a trapping potential, including the existence of pure Mott phases and highly populated condensates. In this paper we show that the ODC method can also lead to temperatures that are smaller than with the conventional DC method, depending on the control parameters. We determine these parameters using exact diagonalizations for the hard-core case, then we extend our results to the soft-core case by performing quantum Monte Carlo (QMC) simulations for both DC and ODC systems at fixed temperatures, and analysing the corresponding entropies. We also propose a method for measuring the entropy in QMC simulations.Comment: 6 pages, 6 figure

Effective algebraic degeneracy

We prove that any nonconstant entire holomorphic curve from the complex line C into a projective algebraic hypersurface X = X^n in P^{n+1}(C) of arbitrary dimension n (at least 2) must be algebraically degenerate provided X is generic if its degree d = deg(X) satisfies the effective lower bound: d larger than or equal to n^{{(n+1)}^{n+5}}

Mott Domains of Bosons Confined on Optical Lattices

In the absence of a confining potential, the boson Hubbard model in its ground state is known to exhibit a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong on-site repulsion. In this paper, we use quantum Monte Carlo simulations to study the ground state of the one dimensional bosonic Hubbard model in a trap. We show that some, but not all, aspects of the Mott insulating phase persist when a confining potential is present. The Mott behavior is present for a continuous range of incommensurate fillings, a very different situation from the unconfined case. Furthermore the establishment of the Mott phase does not proceed via a quantum phase transition in the traditional sense. These observations have important implications for the interpretation of experimental results for atoms trapped on optical lattices. Initial results show that, qualitatively, the same results persist in higher dimensions.Comment: Revtex file, five figures, include

Finite temperature QMC study of the one-dimensional polarized Fermi gas

Quantum Monte Carlo (QMC) techniques are used to provide an approximation-free investigation of the phases of the one-dimensional attractive Hubbard Hamiltonian in the presence of population imbalance. The temperature at which the "Fulde-Ferrell-Larkin-Ovchinnikov" (FFLO) phase is destroyed by thermal fluctuations is determined as a function of the polarization. It is shown that the presence of a confining potential does not dramatically alter the FFLO regime, and that recent experiments on trapped atomic gases likely lie just within the stable temperature range.Comment: 10 pages, 13 figures We added a discussion of the behaviour of the FFLO peak as a function of the attractive interaction strengt

Superfluid and Mott Insulator phases of one-dimensional Bose-Fermi mixtures

We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the Canonical Worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and inter-species interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.Comment: 8 pages, 12 figure

Harold Jeffreys's Theory of Probability Revisited

Published exactly seventy years ago, Jeffreys's Theory of Probability (1939) has had a unique impact on the Bayesian community and is now considered to be one of the main classics in Bayesian Statistics as well as the initiator of the objective Bayes school. In particular, its advances on the derivation of noninformative priors as well as on the scaling of Bayes factors have had a lasting impact on the field. However, the book reflects the characteristics of the time, especially in terms of mathematical rigor. In this paper we point out the fundamental aspects of this reference work, especially the thorough coverage of testing problems and the construction of both estimation and testing noninformative priors based on functional divergences. Our major aim here is to help modern readers in navigating in this difficult text and in concentrating on passages that are still relevant today.Comment: This paper commented in: [arXiv:1001.2967], [arXiv:1001.2968], [arXiv:1001.2970], [arXiv:1001.2975], [arXiv:1001.2985], [arXiv:1001.3073]. Rejoinder in [arXiv:0909.1008]. Published in at http://dx.doi.org/10.1214/09-STS284 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org