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Modern Physics Letters B

DISORDER-INDUCED INSTABILITY OF THE QUANTUM CRITICAL BEHAVIOR OF BOSE FLUIDS

I. P. Takov

Published Feb 28, 2000• 0 citations
Publisher

Abstract

The one-loop renormalization-group equations for Bose fluids with randomly distributed impurities are derived and analyzed with the help of a double ∊-expansion. While the low temperature critical behavior is similar to that of classical systems with extended impurities, the proper quantum critical behavior of disordered Bose fluids at zero temperature is unstable with respect to randomly distributed impurities with short-range correlations.

DOI
10.1142/s0217984900000252

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The one-loop renormalization-group equations for Bose fluids with randomly distributed impurities are derived and analyzed with the help of a double ∊-expansion. While the low temperature critical behavior is similar to that of classical systems with extended impurities, the proper quantum critical behavior of disordered Bose fluids at zero temperature is unstable with respect to randomly distributed impurities with short-range correlations.
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We show that the Bose-glass phase of a one-dimensional disordered Bose fluid exhibits a chaotic behavior, i.e., an extreme sensitivity to external parameters. Using bosonization, the replica formalism and the nonperturbative functional renormalization group, we find that the ground state is unstable to any modification of the disorder configuration ("disorder" chaos) or variation of the Luttinger parameter ("quantum" chaos, analog to the "temperature" chaos in classical disordered systems). This result is obtained by considering two copies of the system, with slightly different disorder configurations or Luttinger parameters, and showing that intercopy statistical correlations are suppressed at length scales larger than an overlap length ξ_{ov}∼|ε|^{-1/α} (|ε|≪1 is a measure of the difference between the disorder distributions or Luttinger parameters of the two copies). The chaos exponent α can be obtained by computing ξ_{ov} or by studying the instability of the Bose-glass fixed point for the two-copy system when ε≠0. The renormalized, functional, intercopy disorder correlator departs from its fixed-point value-characterized by "cuspy" singularities-via a chaos boundary layer, in the same way as it approaches the Bose-glass fixed point when ε=0 through a quantum boundary layer. Performing a linear analysis of perturbations about the Bose-glass fixed point, we find α=1.
The effects of short-range-correlated impurities on the critical behavior of some quantum models with a free-energy spectrum $\ensuremath{\sim}{k}^{\ensuremath{\sigma}}(0<\ensuremath{\sigma}<~2)$ are investigated by using the renormalization-group approach via the replica trick. At zero temperature, two nonsimultaneous expansion parameters ${\ensuremath{\epsilon}}_{q}={d}_{q}\ensuremath{-}d({d}_{q}=\ensuremath{\sigma}$ or $\frac{3}{2}\ensuremath{\sigma}$) and $\ensuremath{\epsilon}=2\ensuremath{\sigma}\ensuremath{-}d$ are involved in terms of which an unusual phase transition is predicted for $d<2\ensuremath{\sigma}$.
We consider a one-dimensional system of interacting bosons in a random potential. At zero temperature, it can be either in the superfluid or in the insulating phase. We study the transition at weak disorder and moderate interaction. Using a systematic approach, we derive the renormalization group equations at two-loop order and discuss the phase diagram. We find the universal form of the correlation functions at the transitions and compute the logarithmic corrections to the main universal power-law behavior. In order to mimic large density fluctuations on a single site, we study a simplified model of disordered two-leg bosonic ladders with correlated disorder across the rung. Contrarily to the single-chain case, the latter system exhibits a transition between a superfluid and a localized phase where the exponents of the correlation functions at the transition do not take universal values.
The critical properties of a ddd-dimensional Bose model in the presence of a random quenched field are investigated by renormalization-group techniques via the replica trick. To first order in $\ensuremath{\epsilon}=6\ensuremath{-}d$ it is found that both at nonzero- and zero-temperature regimes the grand-canonical critical exponents are the same as those of the corresponding classical model so that thermal and quantum fluctuations appear to be irrelevant. Furthermore, at zero temperature, the scaling laws already established for the pure model are retrieved with the replacement of ddd with $d\ensuremath{-}4$, but the random critical exponents are not derivable from the pure ones with the dimensional shift $d\ensuremath{\rightarrow}d\ensuremath{-}4$.
The momentum-shell renormalization group (RG) is used to study the condensation of interacting Bose gases without and with disorder. First of all, for the homogeneous disorder-free Bose gas the interaction-induced shifts in the critical temperature and chemical potential are determined up to second order in the scattering length. The approach does not make use of dimensional reduction and is thus independent of previous derivations. Secondly, the RG is used together with the replica method to study the interacting Bose gas with delta-correlated disorder. The flow equations are derived and found to reduce, in the high-temperature limit, to the RG equations of the classical Landau-Ginzburg model with random-exchange defects. The random fixed point is used to calculate the condensation temperature under the combined influence of particle interactions and disorder.