The critical phenomenon of the zero-temperature superfluid--Bose-glass phase transition for hard-core bosons on a three-dimensional disordered lattice is studied using a quantum real-space renormalization-group method. The correlation-length exponent \ensuremath{\nu} and the dynamic exponent z are computed. The critical exponent z is found to be 2.5 for compressible states and 1.3 for incompressible states. The exponent \ensuremath{\nu} is shown to be insensitive to z as that in the two-dimensional case, and has a value roughly equal to 1.
The critical phenomenon of the zero-temperature superfluid--Bose-glass phase transition for hard-core bosons on a three-dimensional disordered lattice is studied using a quantum real-space renormalization-group method. The correlation-length exponent \ensuremath{\nu} and the dynamic exponent z are computed. The critical exponent z is found to be 2.5 for compressible states and 1.3 for incompressible states. The exponent \ensuremath{\nu} is shown to be insensitive to z as that in the two-dimensional case, and has a value roughly equal to 1.
We investigate the critical phenomena of hard-core bosons in a disordered medium. Such a system is mapped onto a quantum spin-1/2 XY model with transverse random field. The system then is studied through a quantum real-space renormalization-group method. We find that randomness is always relevant in a one-dimensional (1D) system, in agreement with exact results. In two and three dimensions, there is a critical amount of disorder, below which the superfluid phase is stable. In 2D, the dynamic exponent z=1.7 for compressible states, and is close to the value of z=d as predicted by Fisher et al. $z--- is smaller for incompressible states. The correlation length exponent \ensuremath{\nu} is insensitive to z, and roughly equals 1.4. Unlike the superfluid--Mott-insulator transition without disorder, which has two distinct universality classes, we find there is only one universality class for the superfluid--Bose-glass transition.
We determine the dynamical critical exponent z appearing at the Bose glass to superfluid transition in two dimensions by performing large scale numerical studies of two microscopically different quantum models within the universality class: The hard-core boson model and the quantum rotor (soft core) model, both subject to strong on-site disorder. By performing many simulations at different system size L and inverse temperature β close to the quantum critical point, the position of the critical point and the critical exponents, z, ν, and η can be determined independently of any implicit assumptions of the numerical value of z, in contrast to most prior studies. This is done by a careful scaling analysis close to the critical point with a particular focus on the temperature dependence of the scaling functions. For the hard-core boson model we find z=1.88(8), ν=0.99(3), and η=-0.16(8) with a critical field of h(c)=4.79(3), while for the quantum rotor model we find z=1.99(5), ν=1.00(2), and η=-0.3(1) with a critical hopping parameter of t(c)=0.0760(5). In both cases do we find a correlation length exponent consistent with ν=1, saturating the bound ν≥2/d as well as a value of z significantly larger than previous studies, and for the quantum rotor model consistent with z=d.
We present a Monte Carlo study of the Bose glass to superfluid transition in the three-dimensional Bose-Hubbard model. Simulations are performed on the classical (3+1) dimensional link-current representation using the geometrical worm algorithm. Finite-size scaling analysis (on lattices as large as $16\ifmmode\times\else\texttimes\fi{}16\ifmmode\times\else\texttimes\fi{}16\ifmmode\times\else\texttimes\fi{}512$ sites) of the superfluid stiffness and the compressibility is consistent with a value of the dynamical critical exponent z=3, in agreement with existing scaling and renormalization group arguments that z=d. We find also a value of $\ensuremath{\nu}=0.70(12)$ for the correlation length exponent, satisfying the relation $\ensuremath{\nu}\ensuremath{\ge}2∕d$. However, a detailed study of the correlation functions, $C(r,\ensuremath{\tau})$, at the quantum critical point are not consistent with this value of z. We speculate that this discrepancy could be due to the fact that the correlation functions have not reached their true asymptotic behavior because of the relatively small spatial extent of the lattices used in the present study.
Recent experimental and numerical studies of the critical-temperature exponent ϕ for the superfluid-Bose-glass universality in three-dimensional systems report strong violations of the key quantum critical relation, ϕ=νz, where z and ν are the dynamic and correlation-length exponents, respectively; these studies question the conventional scaling laws for this quantum critical point. Using Monte Carlo simulations of the disordered Bose-Hubbard model, we demonstrate that previous work on the superfluid-to-normal-fluid transition-temperature dependence on the chemical potential (or the magnetic field, in spin systems), T_{c}∝(μ-μ_{c})^{ϕ}, was misinterpreting transient behavior on approach to the fluctuation region with the genuine critical law. When the model parameters are modified to have a broad quantum critical region, simulations of both quantum and classical models reveal that the ϕ=νz law [with ϕ=2.7(2), z=3, and ν=0.88(5)] holds true, resolving the ϕ-exponent "crisis."
The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ``ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ``Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential.The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension dc which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on 4He absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.
The ground-state of hard-core bosons in a random one-body potential is studied numerically to observe the transition from superfluid to insulating ``Bose glass'' phase. Finite-size scaling analyses are performed to estimate the transition point and critical exponents. The dynamical critical exponent is z=1.95\ifmmode\pm\else\textpm\fi{}0.25 and is consistent with the prediction of Fisher et al. [Phys. Rev. B 40, 546 (1989)]. Values for other exponents and preliminary results regarding the universal conductivity are presented.