Coherent state wave functions on a torus with a constant magnetic field
2013 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 27, 275302Article in journal (Refereed) Published
We study two alternative definitions of localized states in the lowest Landau level (LLL) on a torus. One definition is to construct localized states, as the projection of the coordinate delta function onto the LLL. Another definition, proposed by Haldane, is to consider the set of functions which have all their zeros at a single point. Since a LLL wave function on a torus, supporting N-phi magnetic flux quanta, is uniquely defined by the position of its N-phi zeros, this defines a set of functions that are expected to be localized around the point maximally far away from the zeros. These two families of localized states have many properties in common with the coherent states on the plane and on the sphere, viz a resolution of unity and a self-reproducing kernel. However, we show that only the projected delta function is maximally localized. Additionally, we show how to project onto the LLL, functions that contain holomorphic derivatives and/or anti-holomorphic polynomials, and apply our methods in the description of hierarchical quantum Hall liquids.
Place, publisher, year, edition, pages
2013. Vol. 46, no 27, 275302
Research subject Theoretical Physics
IdentifiersURN: urn:nbn:se:su:diva-92377DOI: 10.1088/1751-8113/46/27/275302ISI: 000320758400011OAI: oai:DiVA.org:su-92377DiVA: diva2:638688
FunderSwedish Research Council