Critical Theories of the Dissipative Hofstadter Model

TL;DR

This paper investigates the critical behavior of the dissipative Hofstadter model, exploring its free energy, N-point functions, and boundary states, with a focus on how these depend on the magnetic field, revealing new insights into its zero-field case.

Contribution

It provides the first detailed analysis of the critical theories associated with the dissipative Hofstadter model, especially their magnetic field dependence and boundary properties.

Findings

Analyzed the free energy and N-point functions of the critical theory.

Explored the boundary state structure of the model.

Presented new results on the zero magnetic field case.

Abstract

It has recently been shown that the dissipative Hofstadter model (dissipative quantum mechanics of an electron subject to uniform magnetic field and periodic potential in two dimensions) exhibits critical behavior on a network of lines in the dissipation/magnetic field plane. Apart from their obvious condensed matter interest, the corresponding critical theories represent non-trivial solutions of open string field theory, and a detailed account of their properties would be interesting from several points of view. A subject of particular interest is the dependence of physical quantities on the magnetic field since it, much like $\theta_{\rm QCD}$, serves only to give relative phases to different sectors of the partition sum. In this paper we report the results of an initial investigation of the free energy, $N$-point functions and boundary state of this type of critical theory. Although our primary goal is the study of the magnetic field dependence of these quantities, we will present some new results which bear on the zero magnetic field case as well.