Quantum Hall Smectics, Sliding Symmetry and the Renormalization Group

TL;DR

This paper investigates how sliding symmetry affects the low-energy behavior of quantum Hall smectics, revealing that it leads to a fixed point characterized by an array of sliding Luttinger liquids, challenging naive continuum approximations.

Contribution

It demonstrates that sliding symmetry causes the breakdown of naive continuum theory and identifies the correct fixed point as an array of sliding Luttinger liquids using renormalization group analysis.

Findings

Naive continuum approximation breaks down due to infrared divergences.

The correct fixed point is an array of sliding Luttinger liquids.

Sliding symmetry influences the low-energy fixed point structure.

Abstract

In this paper we discuss the implication of the existence of a sliding symmetry, equivalent to the absence of a shear modulus, on the low-energy theory of the quantum hall smectic (QHS) state. We show, through renormalization group calculations, that such a symmetry causes the naive continuum approximation in the direction perpendicular to the stripes to break down through infrared divergent contributions originating from naively irrelevant operators. In particular, we show that the correct fixed point has the form of an array of sliding Luttinger liquids which is free from superficially "irrelevant operators". Similar considerations apply to all theories with sliding symmetries.