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arXiv:cond-mat/9602144 · Journal of Statistical Physics

Long-range correlations and generic scale invariance in classical fluids and disordered electron systems

T. R. Kirkpatrick, D. Belitz

Published Jun 1, 1997• 12 citations
arXivHTMLPDF
DOI
10.1007/bf02181286

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This review discusses a paradigm that has become of increasing importance in the theory of quantum phase transitions, namely, the coupling of the order-parameter fluctuations to other soft modes and the resulting impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms of the order parameter only. The soft modes in question are manifestations of generic scale invariance, i.e., the appearance of long-range order in whole regions in the phase diagram. The concept of generic scale invariance and its influence on critical behavior is explained using various examples, both classical and quantum mechanical. The peculiarities of quantum phase transitions are discussed, with emphasis on the fact that they are more susceptible to the effects of generic scale invariance than their classical counterparts. Explicit examples include the quantum ferromagnetic transition in metals, with or without quenched disorder; the metal-superconductor transition at zero temperature; and the quantum antiferromagnetic transition. Analogies with classical phase transitions in liquid crystals and classical fluids are pointed out, and a unifying conceptual framework is developed for all transitions that are influenced by generic scale invariance.
We introduce a new universal framework describing fluctuations and correlations in quantum and classical many-body systems, at the Euler hydrodynamic scale of space and time. The framework adapts the ideas of the conventional macroscopic fluctuation theory (MFT) to systems that support ballistic transport. The resulting “ballistic MFT” (BMFT) is solely based on the Euler hydrodynamics data of the many-body system. Within this framework, mesoscopic observables are classical random variables depending only on the fluctuating conserved densities, and Euler-scale fluctuations are obtained by deterministically transporting thermodynamic fluctuations via the Euler hydrodynamics. Using the BMFT, we show that long-range correlations in space generically develop over time from long-wavelength inhomogeneous initial states in interacting models. This result, which we verify by numerical calculations, challenges the long-held paradigm that at the Euler scale, fluid cells may be considered uncorrelated. We also show that the Gallavotti-Cohen fluctuation theorem for non-equilibrium ballistic transport follows purely from time-reversal invariance of the Euler hydrodynamics. We check the validity of the BMFT by applying it to integrable systems, and in particular the hard-rod gas, with extensive simulations that confirm our analytical results.
We study the interplay of disorder and interaction effects including bosonic degrees of freedom in the framework of a generic one-dimensional transport model: the Anderson-Edwards model. Using the density-matrix-renormalization group technique, we extract the localization length and the renormalization of the Tomonaga-Luttinger-liquid parameter from the charge-structure factor by a elaborate sample-average finite-size scaling procedure. The properties of the Anderson localized state can be described in terms of scaling relations of the metallic phase without disorder. We analyze how disorder competes with the charge-density-wave correlations triggered by the bosons and give evidence that disorder will destroy the long-range charge-ordered state.