Universität zu Köln

Klevtsov, Semyon (2019). Laughlin States on Higher Genus Riemann Surfaces. Commun. Math. Phys., 367 (3). S. 837 - 872. NEW YORK: SPRINGER. ISSN 1432-0916

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Abstract

Considering quantum Hall states on geometric backgrounds has proved over the past few years to be a useful tool for uncovering their less evident properties, such as gravitational and electromagnetic responses, topological phases, and novel geometric adiabatic transport coefficients. One of the transport coefficients, the central charge associated with the gravitational anomaly, appears as a Chern number for the adiabatic transport on the moduli spaces of higher genus Riemann surfaces. This calls for a better understanding of the QH states on these backgrounds. Here we present a rigorous definition and give a detailed account of the construction of Laughlin states on Riemann surfaces of genus g>1. By the first principles construction we prove that the dimension of the vector space of Laughli states is at least qg for the filling fraction =1/q. Then, using the path integral for the 2d bosonic field compactified on a circle, we reproduce the conjectured qg-degeneracy as the number of independent holomorphic blocks. We also discuss the lowest Landau level, integer QH state and its relation to the bosonization formulas on higher genus Riemann surfaces.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Klevtsov, Semyon UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-149897
DOI:	10.1007/s00220-019-03318-6
Journal or Publication Title:	Commun. Math. Phys.
Volume:	367
Number:	3
Page Range:	S. 837 - 872
Date:	2019
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1432-0916
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language INCOMPRESSIBLE QUANTUM FLUID; FUNCTIONAL DETERMINANTS; GROUND-STATE; HALL STATES; BOSONIZATION; QUANTIZATION; DEGENERACY; TRANSPORT; GEOMETRY; FIELDS Multiple languages Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/14989