2020/11/15 by Janusz Jacak, Jacak, Janusz E.
Materials Science · Physics and Astronomy · #FOS: Physical sciences #Graphene research and applications #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum and electron transport phenomena #Surface and Thin Film Phenomena
paper · pdf · doi:10.48550/arxiv.2011.09945
openalex publication_date 2020/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.