Using an extensive scaling analysis of the transport properties in twinned ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ crystals we have experimentally found the predicted change in the universality class of the Bose-glass to liquid transition when the magnetic field is applied at small angles away from the direction of the correlated defects. The new dynamical critical exponent is ${s}^{\ensuremath{'}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.1\ifmmode\pm\else\textpm\fi{}0.3$.
Using an extensive scaling analysis of the transport properties in twinned YBa2Cu3O7\ensuremath−\ensuremathδ crystals we have experimentally found the predicted change in the universality class of the Bose-glass to liquid transition when the magnetic field is applied at small angles away from the direction of the correlated defects. The new dynamical critical exponent is s\ensuremath′=1.1\ifmmode±\else\textpm\fi0.3.
A demonstration of critical scaling of the magnetic susceptibility in a YBa2Cu3O7 single crystal is performed for 350 frequencies (f) from 1 kHz to 2 MHz. Near the vortex-glass melting temperature TM(H) and in the linear-response limit, the susceptibility \ensuremath{\chi}\ensuremath{\equiv}\ensuremath{\Vert}\ensuremath{\chi}\ensuremath{\Vert}${\mathit{e}}_{\mathrm{\ensuremath{\chi}}}^{\mathit{i}(\mathrm{\ensuremath{\pi}}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\varphi}}}$) follows the scaling relations \ensuremath{\Vert}\ensuremath{\chi}\ensuremath{\Vert}\ensuremath{\sim}\ensuremath{\Vert}1-(T/TM)${\mathrm{\ensuremath{\Vert}}}^{\ensuremath{\nu}/2}$ for f\ensuremath{\rightarrow}0, \ensuremath{\Vert}\ensuremath{\chi}\ensuremath{\Vert}\ensuremath{\sim}f1/(2z) and ${\mathrm{\ensuremath{\varphi}}}_{\mathrm{\ensuremath{\chi}}}$=\ensuremath{\pi}/4z for T\ensuremath{\rightarrow}TM. The static and dynamic exponents (\ensuremath{\nu}\ensuremath{\approxeq}2/3 and z\ensuremath{\approxeq}3) as well as TM(H) are found to be in excellent agreement with our previous dc and ac transport measurements, lending strong support for a second-order phase transition.
We present the scaling relations for a Bose-glass superconductor in the case in which the sample is limited in size in the direction of the correlated defects. In this situation, which corresponds to the experiments found in the literature, we show that there are several differences with the predictions based on an infinite sample size analysis, notably, the usual anisotropy in electrical transport, which was shown to be reversed near the Bose-glass transition, is found to be re-established by the finiteness of the sample. In addition, we also derive the general anisotropic scaling relations for a continuous vortex transition in three dimensions which should be applied, for example, in the case of a single family of parallel twin boundaries.
We study vortex lines in high-temperature superconductors with columnar defects produced by heavy-ion irradiation. We reconsider scaling theory for the Bose-glass transition with tilted magnetic fields, and propose, e.g. , a new scaling form for the shape of the Bose glass phase boundary, which is relevant for experiments. We also consider Monte Carlo simulations for a vortex model with a screened interaction. Critical exponents are determined from scaling analysis of Monte Carlo data for current-voltage characteristics and other quantities. The dynamic critical exponent is found to be z = 4.6 ± 0.3.
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.
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."
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.