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Title: Anyons in conformal Hilbert spaces: statistics and dynamics of gapless excitations in fractional quantum Hall systems
Authors: Yang, Bo
Keywords: Science::Physics
Issue Date: 2022
Source: Yang, B. (2022). Anyons in conformal Hilbert spaces: statistics and dynamics of gapless excitations in fractional quantum Hall systems. International Journal of Modern Physics B, 36(21), 2230003-.
Project: NRF-NRFF12-2020-005
Journal: International Journal of Modern Physics B
Abstract: This paper reviews some of the recent progresses in understanding the dynamical and statistical properties of anyons in fractional quantum Hall (FQH) systems. These are strongly interacting topological systems for electrons confined to a two-dimensional manifold, and anyons are fundamental particles emerging from the truncation of the Hilbert space as a result of both the kinetic and interaction energies. We introduce the concept of the conformal Hilbert spaces (CHS) from such Hilbert space truncation, and the hierarchy of these Hilbert spaces allows us to understand the internal structures of the anyons that can strongly affect their dynamics. The bulk-edge correspondence and the conformal mapping of the CHS also enable us to derive a rigorous bosonization scheme for anyons in these two-dimensional systems, and to capture the statistical interaction between anyons in the form of microscopic interaction Hamiltonians. Examples about the fractionalization of Laughlin quasiholes and a new family of bosonic FQH phases as the dual descriptions of the well-known fermionic FQH phases are given, as applications to the proposed theoretical constructions in this work.
ISSN: 0217-9792
DOI: 10.1142/S0217979222300031
Schools: School of Physical and Mathematical Sciences 
Rights: © 2022 World Scientific Publishing Company. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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