The Infinite Symmetry and Interplay Between Integer and Fractional Quantum Hall Effect
M.Eliashvili
TL;DR
This paper explores the deep mathematical relationship between integer and fractional quantum Hall effects through spectrum generating algebras and complex Chern-Simons gauge fields, revealing a unified theoretical framework.
Contribution
It introduces a non-unitary similarity transformation linking the wave functions of integer and fractional quantum Hall effects via complex Chern-Simons gauge fields.
Findings
Spectrum generating algebras for IQHE and FQHE are related by a non-unitary transformation.
Complex Chern-Simons gauge fields underpin the second quantization of FQHE.
Unified mathematical framework for IQHE and FQHE established.
Abstract
It is shown, that a spectrum generating algebras and wave functions for the integral and fractional quantum Hall effect are related by the non-unitary similarity transformation. This transformation corresponds to the introduction of the complex Chern-Simons gauge fields, in terms of which the second quantized form of FQHE can be developed
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Taxonomy
TopicsQuantum and electron transport phenomena · Mechanical and Optical Resonators · Surface and Thin Film Phenomena