Probing the geometry of the Laughlin state

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 sim...

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Bibliographic Details
Published in:New journal of physics 2016-02, Vol.18 (2), p.25011
Main Authors: Johri, Sonika, Papić, Z, Schmitteckert, P, Bhatt, R N, Haldane, F D M
Format: Article
Language:English
Subjects:
73.43.Cd
73.43.Lp
Anisotropy
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Deformation
Degrees of freedom
Electric fields
fractional quantum Hall effect
Geometry
Laughlin wave function
Long range order
Mathematical analysis
Physics
quantum geometry
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Summary: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 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.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/18/2/025011