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Title: 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 simplest example of fractional quantumHall states—the filling v = 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. Furthermore, 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.
Authors:
 [1] ;  [2] ;  [3] ;  [1] ;  [1]
  1. Princeton Univ., Princeton, NJ (United States)
  2. Univ. of Leeds, Leeds (United Kingdom)
  3. Karlsruhe Institute of Technology, Eggenstien-Leopoldshafen (Gemany); Heinrich-Heine-Univ., Dusseldorf (Germany)
Publication Date:
OSTI Identifier:
1255131
Grant/Contract Number:
SC0002140
Type:
Accepted Manuscript
Journal Name:
New Journal of Physics
Additional Journal Information:
Journal Volume: 18; Journal Issue: 2; Journal ID: ISSN 1367-2630
Publisher:
IOP Publishing
Research Org:
Princeton Univ., Princeton, NJ (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS