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Exact matrix product states for quantum Hall wave functions

Zaletel, Michael P. and Mong, Roger S. K. (2012) Exact matrix product states for quantum Hall wave functions. Physical Review B, 86 (24). Art. No. 245305. ISSN 1098-0121. doi:10.1103/PhysRevB.86.245305.

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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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Additional Information:© 2012 American Physical Society. Received 29 August 2012; published 11 December 2012. We would like to acknowledge helpful conversations with Joel E. Moore, Tarun Grover, Frank Pollmann, Sid Parameswaran, and Jérôme Dubail, as well as support from NSF GRFP Grant No. DGE 1106400 (M.Z.) and NSF DMR-0804413 (R.M.).
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Issue or Number:24
Classification Code:PACS: 73.43.Cd, 03.67.Mn, 05.30.Pr
Record Number:CaltechAUTHORS:20130115-141527135
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36400
Deposited By: John Wade
Deposited On:15 Jan 2013 22:40
Last Modified:09 Nov 2021 23:22

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