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On the particle entanglement spectrum of the Laughlin states
Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
Stockholm University, Faculty of Science, Department of Physics.
Number of Authors: 3
2015 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, no 28, 285205Article in journal (Refereed) Published
Abstract [en]

The study of the entanglement entropy and entanglement spectrum has proven to be very fruitful in identifying topological phases of matter. Typically, one performs numerical studies of finite-size systems. However, there are few rigorous results in this regard. We revisit the problem of determining the rank of the 'particle entanglement spectrum' (PES) of the Laughlin states. We reformulate the problem into a problem concerning the ideal of symmetric polynomials that vanish under the formation of several clusters of particles. We introduce an explicit generating set of this ideal, and we prove that polynomials in this ideal have a total degree that is bounded from below. We discuss the difficulty in proving the same bound on the degree of any of the variables, which is necessary to determine the rank of the PES.

Place, publisher, year, edition, pages
2015. Vol. 48, no 28, 285205
Keyword [en]
entanglement spectrum, quantum Hall effect, Laughlin state
National Category
Physical Sciences Mathematics
URN: urn:nbn:se:su:diva-119287DOI: 10.1088/1751-8113/48/28/285205ISI: 000357281400009OAI: diva2:844249
Available from: 2015-08-04 Created: 2015-08-03 Last updated: 2015-08-04Bibliographically approved

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Majidzadeh Garjani, BabakArdonne, Eddy
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