Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems

We prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder. We also prove compressibility of the system on the superfluid--insulator critical line and in its neighborhood. These conclusions follow from a general {\it theorem of inclusions} which states that for any transition in a disordered system one can always find rare regions of the competing phase on either side of the transition line. Quantum Monte Carlo simulations for the disordered Bose-Hubbard model show an even stronger result, important for the nature of the Mott insulator to Bose glass phase transition: The critical disorder bound, $\Delta_c$, corresponding to the onset of disorder-induced superfluidity, satisfies the relation $\Delta_c > E_{\rm g/2}$, with $E_{\rm g/2}$ the half-width of the Mott gap in the pure system.Comment: 4 pages, 3 figures; replaced with resubmitted versio

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

Labor Relations in the Conditions of Digitization of The Economy

The article analyses modern tendencies of development of the digital economy, given their role in the development of society and, as a consequence, in the transformation of socio-economic relations. The goal is to identify the main directions of training in the digital environment. It is shown that in addition to training professionals in the IT industry is required a high-quality training in the field of management, i.e. in the area of systems-organization of interaction of the ecosystem of people and machines, where routine operations will be done by machines, intelligent control and regulatory function management

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

The fate of vacancy-induced supersolidity in 4He

The supersolid state of matter, exhibiting non-dissipative flow in solids, has been elusive for thirty five years. The recent discovery of a non-classical moment of inertia in solid 4He by Kim and Chan provided the first experimental evidence, although the interpretation in terms of supersolidity of the ideal crystal phase remains subject to debate. Using quantum Monte Carlo methods we investigate the long-standing question of vacancy-induced superflow and find that vacancies in a 4He crystal phase separate instead of forming a supersolid. On the other hand, non-equilibrium vacancies relaxing on defects of poly-crystalline samples could provide an explanation for the experimental observations.Comment: 4 pages,4 figures. Replaced with published versio

Phase diagram of the disordered Bose-Hubbard model

We establish the phase diagram of the disordered three-dimensional Bose-Hubbard model at unity filling, which has been controversial for many years. The theorem of inclusions, proven in Ref. [1], states that the Bose glass phase always intervenes between the Mott insulating and superfluid phases. Here, we note that assumptions on which the theorem is based exclude phase transitions between gapped (Mott insulator) and gapless phases (Bose glass). The apparent paradox is resolved through a unique mechanism: such transitions have to be of the Griffiths type when the vanishing of the gap at the critical point is due to a zero concentration of rare regions where extreme fluctuations of disorder mimic a {\it regular} gapless system. An exactly solvable random transverse field Ising model in one dimension is used to illustrate the point. A highly non-trivial overall shape of the phase diagram is revealed with the worm algorithm. The phase diagram features a long superfluid finger at strong disorder and on-site interaction. Moreover, bosonic superfluidity is extremely robust against disorder in a broad range of interaction parameters; it persists in random potentials nearly 50 (!) times larger than the particle half-bandwidth. Finally, we comment on the feasibility of obtaining this phase diagram in cold-atom experiments, which work with trapped systems at finite temperature.Comment: 9 pages, 5 figure

Differential approximation for Kelvin-wave turbulence

I present a nonlinear differential equation model (DAM) for the spectrum of Kelvin waves on a thin vortex filament. This model preserves the original scaling of the six-wave kinetic equation, its direct and inverse cascade solutions, as well as the thermodynamic equilibrium spectra. Further, I extend DAM to include the effect of sound radiation by Kelvin waves. I show that, because of the phonon radiation, the turbulence spectrum ends at a maximum frequency $\omega^* \sim (\epsilon^3 c_s^{20} / \kappa^{16})^{1/13}$ where $\epsilon$ is the total energy injection rate, $c_s$ is the speed of sound and $\kappa$ is the quantum of circulation.Comment: Prepared of publication in JETP Letter

Diagrammatic Monte Carlo for Correlated Fermions

We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC) can be used for tackling hard fermionic quantum many-body problems in the thermodynamic limit by presenting accurate results for the repulsive Hubbard model in the correlated Fermi liquid regime. Sampling Feynman's diagrammatic series for the single-particle self-energy we can study moderate values of the on-site repulsion ($U/t \sim 4$) and temperatures down to $T/t=1/40$. We compare our results with high temperature series expansion and with single-site and cluster dynamical mean-field theory.Comment: 4 pages, 5 figures, stylistic change

Superfluid--Insulator Transition in Commensurate Disordered Bosonic Systems:Large-Scale Worm-Algorithm Simulations

We report results of large-scale Monte Carlo simulations of superfluid--insulator transitions in commensurate 2D bosonic systems. In the case of off-diagonal disorder (quantum percolation), we find that the transition is to a gapless incompressible insulator, and its dynamical critical exponent is $z=1.65 \pm 0.2$. In the case of diagonal disorder, we prove the conjecture that rare statistical fluctuations are inseparable from critical fluctuations on the largest scales and ultimately result in the crossover to the generic universality class (apparently with $z=2$). However, even at strong disorder, the universal behavior sets in only at very large space-time distances. This explains why previous studies of smaller clusters mimicked a direct superfluid--Mott-insulator transition.Comment: 6 pages, Latex, 7 figure