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Rigidity of the Laughlin Liquid.

Elliott H Lieb1, Nicolas Rougerie2, Jakob Yngvason3

  • 11Departments of Mathematics and Physics, Princeton University, Princeton, NJ 08544 USA.

Journal of Statistical Physics
|April 19, 2019
PubMed
Summary
This summary is machine-generated.

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Perturbations to the Laughlin state, a key quantum system, cannot increase its particle density beyond a maximum. This finding impacts understanding how these correlated states respond to external fields.

Area of Science:

  • Quantum Hall Effect
  • Condensed Matter Physics

Background:

  • The Laughlin state is a fundamental model for strongly correlated electron systems in the lowest Landau level.
  • Understanding perturbations is crucial for characterizing the stability and response of these quantum states.

Purpose of the Study:

  • To investigate the general form of N-particle wave functions derived from the Laughlin state under perturbation.
  • To determine the impact of external potentials or impurities on the Laughlin state's properties within the lowest Landau level.

Main Methods:

  • Considered N-particle wave functions as a product of the Laughlin state and an analytic function.
  • Analyzed the behavior of the 1-particle density under these perturbations.

Main Results:

Keywords:
Classical Coulomb gasFractional quantum Hall effectLaughlin wave function

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  • Demonstrated that perturbations can only shift or decrease the 1-particle density.
  • Established an upper bound for the 1-particle density, which cannot be exceeded.

Conclusions:

  • The inherent correlations of the Laughlin state impose a strict limit on density changes due to perturbations.
  • These results provide insights into the response of strongly correlated quantum systems to external influences.