Critical Temperature Shift in Weakly Interacting Bose Gas

With a high-performance Monte Carlo algorithm we study the interaction-induced shift of the critical point in weakly interacting three-dimensional $|\psi|^4$-theory (which includes quantum Bose gas). In terms of critical density, $n_c$, mass, $m$, interaction, $U$, and temperature, $T$, this shift is universal: $\Delta n_c(T) = - C m^3 T^2 U$, the constant $C$ found to be equal to $0.0140 \pm 0.0005$. For quantum Bose gas with the scattering length $a$ this implies $\Delta T_c/T_c = C_0 a n^{1/3}$, with $C_0=1.29 \pm 0.05$.Comment: 4 pages, latex, 3 figure

Commensurate Two-Component Bosons in Optical Lattice: Groundstate Phase Diagram

Two sorts of bosons in an optical lattice at commensurate filling factors can form five stable superfluid and insulating groundstates with rich and non-trivial phase diagram. The structure of the groundstate diagram is established by mapping $d$-dimensional quantum system onto a $(d+1)$-dimensional classical loop-current model and Monte Carlo simulations of the latter. Surprisingly, the quantum phase diagram features, besides second-order lines, a first-order transition and two multi-critical points. We explain why first-order transitions are generic for models with paring interactions using microscopic and mean-field arguments.Comment: 4 RevTex pages, 3 ps-figures; replaced with revised version accepted by PRL: results of the MC simulations in 4D are briefly discusse

Worm Algorithm for Continuous-space Path Integral Monte Carlo Simulations

We present a new approach to path integral Monte Carlo (PIMC) simulations based on the worm algorithm, originally developed for lattice models and extended here to continuous-space many-body systems. The scheme allows for efficient computation of thermodynamic properties, including winding numbers and off-diagonal correlations, for systems of much greater size than that accessible to conventional PIMC. As an illustrative application of the method, we simulate the superfluid transition of Helium-four in two dimensions.Comment: Fig. 2 differs from that of published version (includes data for larger system sizes

On the Supersolid State of Matter

We prove that the necessary condition for a solid to be also a superfluid is to have zero-point vacancies, or interstitial atoms, or both, as an integral part of the ground state. As a consequence, superfluidity is not possible in commensurate solids which break continuous translation symmetry. We discuss recent experiment by Kim and Chan [Nature, {\bf 427}, 225 (2004)] in the context of this theorem, question its bulk supersolid interpretation, and offer an alternative explanation in terms of superfluid helium interfaces.Comment: 4 figures, 4 page

Groundstates of SU(2)-Symmetric Confined Bose Gas: Trap for a Schr\"odinger Cat

Conservation of the total isotopic spin S of a two-component Bose gas-like $^{87}$Rb-has a dramatic impact on the structure of the ground state. In the case when S is much smaller than the total number of particles N, the condensation of each of the two components occurs into two single-particle modes. The quantum wavefunction of such a groundstate is a Schr\"odinger Cat-a superposition of the phase separated classical condensates, the most "probable" state in the superposition corresponding to the classical groundstate in the sector of given N and S. After measurement of the spatial distribution of the densities of the two components, the Cat collapses into one of the classical condensate states.Comment: 5 RevTex pages, no figures; replaced with revised version, where the discussion on stability against temporal white noise and losses is adde

Comment on ``One-Dimensional Disordered Bosonic Hubbard Model: A Density-Matrix Renormalization Group Study"

We present the phase diagram of the system obtained by continuous-time worldline Monte Carlo simulations, and demonstrate that the actual phase diagram is in sharp contrast with that found in Phys. Rev. Lett., 76 (1996) 2937.Comment: 1 page, LaTex, 1 figur