Johri, S, Papic, Z, Schmitteckert, P et al. (2 more authors) (2016) Probing the geometry of the Laughlin state. New Journal of Physics, 18. ISSN 1367-2630
Abstract
It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive numerical studies of the geometric degree of freedom for the simplest example of fractional quantum Hall states -- the filling $\nu=1/3$ Laughlin state. We perturb the system by a smooth, spatially dependent metric deformation and measure the response of the Hall fluid, finding it to be proportional to the Gaussian curvature of the metric. Further, we generalize the concept of coherent states to formulate the bulk off-diagonal long range order for the Laughlin state, and compute the deformations of the metric in the vicinity of the edge of the system. We introduce a "pair amplitude" operator and show that it can be used to numerically determine the intrinsic metric of the Laughlin state. These various probes are applied to several experimentally relevant settings that can expose the quantum geometry of the Laughlin state, in particular to systems with mass anisotropy and in the presence of an electric field gradient.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 The Author(s) Creative Commons Attribution 3.0 licence. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds) > Theoretical Physics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 Jan 2016 14:00 |
Last Modified: | 15 Apr 2016 13:18 |
Published Version: | http://dx.doi.org/10.1088/1367-2630/18/2/025011 |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1088/1367-2630/18/2/025011 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:93921 |