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Boundary Effective Action for Quantum Hall States.

Andrey Gromov1,2, Kristan Jensen3, Alexander G Abanov1,4

  • 1Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA.

Physical Review Letters
|April 9, 2016
PubMed
Summary
This summary is machine-generated.

We studied quantum Hall states and their boundary physics, finding four Chern-Simons terms. Two terms describe conductance, while others relate to boundary response, like Hall viscosity, which can change at interfaces.

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Area of Science:

  • Condensed Matter Physics
  • Topological Phases of Matter

Background:

  • Quantum Hall states exhibit unique boundary phenomena.
  • Symmetries play a crucial role in determining these edge physics properties.

Purpose of the Study:

  • To analyze the low-energy effective action of quantum Hall states on spaces with boundaries.
  • To identify symmetry-determined aspects of edge physics.
  • To investigate the role of Chern-Simons terms in Hall conductance and viscosity.

Main Methods:

  • Analysis of the low-energy effective action for quantum Hall states.
  • Focus on Chern-Simons type terms and their implications for boundary phenomena.
  • Examination of symmetry constraints on edge modes and local boundary response.

Main Results:

  • Identified four distinct Chern-Simons terms in the effective action.
  • Two terms are linked to gapless edge modes, describing Hall and thermal Hall conductance.
  • Two terms, including the Wen-Zee term, relate to local boundary response and Hall viscosity, without protecting edge modes.
  • Demonstrated that the Wen-Zee term's coefficient can vary across an interface without breaking symmetries or closing the bulk gap.

Conclusions:

  • Symmetries dictate key features of quantum Hall edge physics.
  • Chern-Simons terms govern both protected edge modes and symmetry-fixed local responses.
  • The Wen-Zee term's behavior at interfaces offers insights into topological phase transitions and material properties.