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Exact matrix product states for quantum Hall wave functions

Michael P. Zaletel and Roger S. K. Mong
Phys. Rev. B 86, 245305 – Published 11 December 2012

Abstract

We show that the model wave functions used to describe the fractional quantum Hall effect have exact representations as matrix product states (MPS). These MPS can be implemented numerically in the orbital basis of both finite and infinite cylinders, which provides an efficient way of calculating arbitrary observables. We extend this approach to the charged excitations and numerically compute their Berry phases. Finally, we present an algorithm for numerically computing the real-space entanglement spectrum starting from an arbitrary orbital basis MPS, which allows us to study the scaling properties of the real-space entanglement spectra on infinite cylinders. The real-space entanglement spectrum obeys a scaling form dictated by the edge conformal field theory, allowing us to accurately extract the two entanglement velocities of the Moore-Read state. In contrast, the orbital space spectrum is observed to scale according to a complex set of power laws that rule out a similar collapse.

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  • Received 29 August 2012

DOI:https://doi.org/10.1103/PhysRevB.86.245305

©2012 American Physical Society

Authors & Affiliations

Michael P. Zaletel1 and Roger S. K. Mong2

  • 1Department of Physics, University of California, Berkeley, California 94720, USA
  • 2Department of Physics, California Institute of Technology, Pasadena, California 91125, USA

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Issue

Vol. 86, Iss. 24 — 15 December 2012

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