Investigating Anisotropic Quantum Hall States with Bimetric Geometry

Area of Science:

• Condensed Matter Physics
• Quantum Hall Effect Physics

Background:

• Fractional quantum Hall (FQH) states exhibit complex topological orders.
• Anisotropy in FQH states introduces challenges for theoretical descriptions.
• Existing models may not fully capture the interplay of geometry and quantum effects.

Purpose of the Study:

• To construct a low-energy effective theory for anisotropic FQH states.
• To establish a relationship between key physical quantities like Hall viscosity and anisotropy.
• To clarify theoretical ambiguities regarding nematic order in FQH systems.

Main Methods:

• Development of a formalism analogous to the bimetric approach in massive gravity.
• Application of the formalism to Abelian anisotropic FQH states under external backgrounds.
• Numerical computation of Hall viscosity using the density matrix renormalization group (DMRG).

Main Results:

• Derivation of a relationship linking shift, Hall viscosity, and a new coupling, anisospin.
• Numerical verification of the derived relationship for various anisotropic FQH states.
• Clarification of the interpretation of the Berry phase term coefficient in nematic effective actions.

Conclusions:

• The developed effective theory provides a unified framework for anisotropic FQH states.
• Anisospin emerges as a crucial quantized coupling characterizing anisotropy.
• The study resolves long-standing disagreements concerning nematic order in the literature.