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Central charge from adiabatic transport of cusp singularities in the quantum Hall effect
- Publication Year :
- 2016
-
Abstract
- We study quantum Hall (QH) states on a punctured Riemann sphere. We compute the Berry curvature under adiabatic motion in the moduli space in the large N limit. The Berry curvature is shown to be finite in the large N limit and controlled by the conformal dimension of the cusp singularity, a local property of the mean density. Utilizing exact sum rules obtained from a Ward identity, we show that for the Laughlin wave function, the dimension of a cusp singularity is given by the central charge, a robust geometric response coefficient in the QHE. Thus, adiabatic transport of curvature singularities can be used to determine the central charge of QH states. We also consider the effects of threaded fluxes and spin-deformed wave functions. Finally, we give a closed expression for all moments of the mean density in the integer QH state on a punctured disk.<br />51 pages, 2 figures
- Subjects :
- Statistics and Probability
High Energy Physics - Theory
General Physics and Astronomy
FOS: Physical sciences
Quantum Hall effect
Curvature
01 natural sciences
Conformal dimension
Condensed Matter - Strongly Correlated Electrons
0103 physical sciences
0101 mathematics
010306 general physics
Adiabatic process
Mathematical Physics
Mathematical physics
Cusp (singularity)
Physics
Strongly Correlated Electrons (cond-mat.str-el)
010102 general mathematics
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
High Energy Physics - Theory (hep-th)
Modeling and Simulation
Gravitational singularity
Berry connection and curvature
Central charge
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....66a5caf9eee61bbf7520748f907181f4