Homotopy quantum phase transitions

TL;DR

This paper introduces a novel class of quantum phase transitions characterized by topological changes in multi-particle systems, specifically using homotopy theory, and illustrates this concept with fractional quantum Hall states.

Contribution

It proposes a new framework for quantum phase transitions based on homotopy topology, distinct from traditional symmetry-breaking approaches.

Findings

Homotopy phases correspond to different quantum incompressible states.

Energy levels change in a step-wise manner across homotopy phases.

The concept is exemplified in fractional quantum Hall states with experimental relevance.

Abstract

We present a new class of quantum phase transitions that refer neither to local order parameter and critical fluctuations nor to continuous symmetry breaking but are assigned by the step-wise change in topology of the multi-particle system expressed in homotopy terms. The energy for homotopy phases changes in a step-wise manner and the different homotopies induce specific correlations in planar interacting multi-particle system representing different commesurability patterns of quantum incompressible states. We illustrate the concept of the homotopy phase transition in the simplest quantum multi-particle system of two repulsing electrons on a 2D finite jellium exposed to a strong perpendicular magnetic field. The homotopy phases related to fractional quantum Hall states are described and compared with their experimental manifestation.