Quantum phase transitions in quantum Hall and other topological systems: role of the Planckian time

TL;DR

This paper demonstrates that the Planckian time scale governs quantum phase transitions in topological systems, including quantum Hall effects and insulators, by explaining experimental data through a phenomenological model that accounts for interactions.

Contribution

It introduces a model linking the Planckian time to quantum phase transitions in interacting topological systems, providing a unified explanation across different dimensions and systems.

Findings

Quantitative agreement with experimental data for integer and fractional QHE.

Model explains QPTs in anomalous QHE, axion, and Chern insulators.

Planckian time is a universal characteristic of QPTs in interacting systems.

Abstract

Transformations between the plateau states of the quantum Hall effect (QHE) are an archetypical example of quantum phase transitions (QPTs) between phases with non-trivial topological order. These transitions appear to be well-described by the single-particle network theories. The long-standing problem with this approach is that it does not account for Coulomb interactions. In this paper, we show that experimental data in the quantum critical regime for both integer and fractional QHEs can be quantitatively explained by the recently developed phenomenological model of QPTs in interacting systems. This model assumes that all effects of interactions are contained in the life-time of fluctuations as set by the Planckian time $\tau_P=\hbar/k_BT$. The dephasing length is taken as the distance traveled by a non-interacting particle along the bulk edge state over this time. We show that the model also provides quantitative description of QPTs between the ground states of anomalous QHE and axion and Chern insulators. These analyzed systems are connected in that the QPTs occur via quantum percolation. Combining the presented results with the results of two companion papers, we conclude that the Planckian time is the encompassing characteristic of QPTs in interacting systems, independent of dimensionality and microscopic physics.