Fixed Points of the Dissipative Hofstadter Model

TL;DR

This paper investigates the phase diagram of a dissipative particle in a magnetic field, revealing a non-trivial fixed point that governs the system's behavior across different regimes, with implications for understanding dissipative quantum systems.

Contribution

It identifies and characterizes a non-trivial fixed point in the dissipative Hofstadter model using exact and variational methods, and discusses an intermediate energy scale separating different physical regimes.

Findings

Existence of a non-trivial fixed point for half flux per plaquette.

Characterization of the fixed point via exact and variational methods.

Identification of an intermediate energy scale separating regimes.

Abstract

The phase diagram of a dissipative particle in a periodic potential and a magnetic field is studied in the weak barrier limit and in the tight-biding regime. For the case of half flux per plaquette, and for a wide range of values of the dissipation, the physics of the model is determined by a non trivial fixed point. A combination of exact and variational results is used to characterize this fixed point. Finally, it is also argued that there is an intermediate energy scale that separates the weak coupling physics from the tight-binding solution.