Sliding phases in U(1) symmetric systems -- mirage of the renormalization group

TL;DR

This paper critically examines the existence of sliding phases in layered U(1) symmetric systems, challenging previous RG predictions through Monte Carlo simulations and analytical arguments, and proposes an alternative long-range interaction model.

Contribution

It demonstrates that sliding phases do not occur in the studied models, contradicting earlier RG-based predictions, and introduces a new model with long-range interactions to realize such phases.

Findings

Monte Carlo simulations show no evidence of sliding phases in the tested layered model.

The results align with an analytical solution indicating the absence of sliding phases.

A new model with long-range interactions is proposed as a potential way to realize sliding phases.

Abstract

We analyse the proposal of sliding phases (SP) in layers hosting global U(1) symmetric variables with finite inter-layer Josephson coupling. Based on the Kosterlitz-Thouless renormalization group (RG) approach, such phases were predicted to exist in various layered (or 1D quantum coupled) systems. The key in the RG argument is treating the coupling as though the variables are non-compact. Large scale Monte Carlo simulations of a layered model, where the SP is supposed to exist, finds no indication of such a phase. Instead, 3D behavior is observed. This result is consistent with the asymptotically exact analytical solution. A generic argument against SP in translationally invariant systems with short range interactions is provided. We have also suggested an alternative model for the SP -- adding long-range interactions to the inter-layer Josephson term.