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Birkhäuser Basel eBooks

Sliding Phases: From DNA-lipid Complexes to Smectic Metals

T. C. Lubensky

Published Jan 1, 2003• 0 citations
Publisher

Abstract

Materials consisting of a stack of “two-dimensional” layers that exhibit 2D power-law order in the absence of coupling between layers include systems as diverse as layered magnets, DNA-lipid complexes, and coupled Luttinger liquids. It is common belief that these systems exhibit “three-dimensional” order whenever there is a nonvanishing interlayer coupling. However, with appropriately chosen interlayer gradient couplings between layers, they can exhibit unusual equilibrium “Sliding Phases” characterized by 2D-like power-law correlations. After reviewing the various types of sliding phases that can occur, this paper will discuss in detail the properties of the simplest sliding phases, the sliding xy phases in three-dimensional stacks of planar xy models. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/978-3-0348-7907-1_54

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Materials consisting of a stack of “two-dimensional” layers that exhibit 2D power-law order in the absence of coupling between layers include systems as diverse as layered magnets, DNA-lipid complexes, and coupled Luttinger liquids. It is common belief that these systems exhibit “three-dimensional” order whenever there is a nonvanishing interlayer coupling. However, with appropriately chosen interlayer gradient couplings between layers, they can exhibit unusual equilibrium “Sliding Phases” characterized by 2D-like power-law correlations. After reviewing the various types of sliding phases that can occur, this paper will discuss in detail the properties of the simplest sliding phases, the sliding xy phases in three-dimensional stacks of planar xy models. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We show that three-dimensional ``sliding'' analogs of the Kosterlitz-Thouless phase, in stacked classical two-dimensional XY\mathrm{XY}XY models and quantum systems of coupled Luttinger liquids, can be enlarged by the application of a parallel magnetic field, which has the effect of increasing the scaling dimensions of the most relevant operators that can perturb the critical sliding phases. Within our renormalization-group analysis, we also find that for the case of coupled Luttinger liquids, this effect is interleaved with the onset of the integer quantum Hall effect for weak interactions and fields. We comment on experimental implications for a conjectured smectic metal phase in the cuprates.
The intent of my project is to determine if the proposal of sliding phases in XY layered systems has physical ground. It will be done by comparing numerical and analytical results for a layered XY models. Sliding phases were first proposed in the context of DNA complexes and then extended to XY models, 1D coupled wires and superfluid films. The existence of the sliding phase would mean that there is a phase transition from 3D to 2D behavior. Such systems have been studied both in the clean case and with disorder. The idea of the sliding phases is based on applying the criterion of relevancy of Josephson coupling between layers along the line of the Sine-Gordon model. Such a criterion is, strictly speaking, valid for a non-compact variable while the XY model is defined for compact one. Thus, it is not clear if this approximation has any validity. Our analysis of the numerical data obtained within Monte Carlo simulations of a model showed that the scaling behavior of the Josephson coupling disagrees qualitatively (and quantitatively) with the flow equation derived from the renormalization group (RG) prediction. Instead of the 3D to 2D phase transition predicted by the RG we see the behavior consistent with the system retaining its 3D character. Our approach is based on the language of duality. It allows reformulating the model in terms of the objects amenable to effective large scale simulations. Furthermore, using this language it becomes possible to formulate a general criterion for the sliding phases to exist – which conspicuously demonstrates that the RG approach is incorrect when applied to the situations of the dimensional reduction. The dual approach allows finding the asymptotically exact analytical solution of the model for clean and disordered cases. It is also suggested how to achieve sliding phases – by introducing effective gauge type interaction between Josephson currents mediated by some soft mode which does not affect currents along the planes.
We study systems of coupled spin-gapped and gapless Luttinger liquids. First, we establish the existence of a sliding Luttinger liquid phase for a system of weakly coupled parallel quantum wires, with and without disorder. It is shown that the coupling can stabilize a Luttinger liquid phase in the presence of disorder. We then extend our analysis to a system of crossed Luttinger liquids and establish the stability of a non-Fermi-liquid state: the crossed sliding Luttinger liquid phase. In this phase the system exhibits a finite-temperature, long-wavelength, isotropic electric conductivity that diverges as a power law in temperature T as $\stackrel{\ensuremath{\rightarrow}}{T}0.$ This two-dimensional system has many properties of a true isotropic Luttinger liquid, though at zero temperature it becomes anisotropic. An extension of this model to a three-dimensional stack exhibits a much higher in-plane conductivity than the conductivity in a perpendicular direction.
We revise a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in two- or three-dimensional arrays in the absence of a magnetic field. We analyse whether physically justifiable (reasonable) inter-wire interactions, i.e. either the screened Coulomb or "Coulomb-blockade" type interactions, stabilise the SLL phase. Calculating the scaling dimensions of the most relevant perturbations (the inter-wire single-particle hybridisation, charge-density wave, and superconducting inter-wire couplings), we find that their combination always destroys the SLL phase for the repulsive intra-wire interaction. However, suppressing the inter-wire tunnelling of repulsive fermions (when the charge-density wave is the only remaining perturbation), one can observe a stability region emerging due to the inter-wire forward scattering interaction.
We revise a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in two- or three-dimensional arrays in the absence of a magnetic field. We analyse whether physically justifiable (reasonable) inter-wire interactions, i.e. either the screened Coulomb or 'Coulomb-blockade' type interactions, stabilise the SLL phase. Calculating the scaling dimensions of the most relevant perturbations (the inter-wire single-particle hybridisation, charge-density wave, and superconducting inter-wire couplings), we find that their combination always destroys the SLL phase for the repulsive intra-wire interaction. However, suppressing the inter-wire tunnelling of repulsive fermions (when the charge-density wave is the only remaining perturbation), one can observe a stability region emerging due to the inter-wire forward scattering interaction.