Date of Degree

2-2020

Document Type

Dissertation

Degree Name

Ph.D.

Program

Physics

Advisor

Anatoly Kuklov

Committee Members

Eugene Chudnovsky

Roman Kezerashvili

Alfred Levine

Vadim Oganesyan

David Schmeltzer

Subject Categories

Condensed Matter Physics | Quantum Physics | Statistical, Nonlinear, and Soft Matter Physics

Abstract

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.

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