Geometrical description of the fractional quantum Hall effect.

  title={Geometrical description of the fractional quantum Hall effect.},
  author={F. D. M. Haldane},
  journal={Physical review letters},
  volume={107 11},
  • F. Haldane
  • Published 17 June 2011
  • Physics, Medicine
  • Physical review letters
The fundamental collective degree of freedom of fractional quantum Hall states is identified as a unimodular two-dimensional spatial metric that characterizes the local shape of the correlations of the incompressible fluid. Its quantum fluctuations are controlled by a topologically quantized "guiding-center spin." Charge fluctuations are proportional to its Gaussian curvature. 

Topics from this paper

Quantum Geometry and Topology
Attempts to understand the phenomenon of the robustness of the values of the Hall conductivity in quantum Hall systems led to the idea of characterizing the ground state of many electron systems
Chiral Gravitons in Fractional Quantum Hall Liquids.
It is demonstrated that they are chiral gravitons carrying angular momentum -2, which are quanta of quantum motion of an internal metric, and show up as resonance peaks in the system's response to what is the fractional Hall analog of gravitational waves.
Geometric response of quantum Hall states to electric fields
Exploiting novel aspects of the quantum geometry of charged particles in a magnetic field via gauge-invariant variables, we provide tangible connections between the response of quantum Hall fluids to
Single-mode approximation for quantum Hall states with broken rotational symmetry
A topological phase can often be represented by a corresponding wavefunction (exact eigenstate of a model Hamiltonian) that has a higher underlying symmetry than necessary. When the symmetry is
Quantum Hall physics : Hierarchies and conformal field theory techniques
The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past 30 years, has generated many ground-breaking new ideas and concepts. Very ear
Integer quantum Hall effect with an anisotropic Coulomb interaction potential
Abstract We consider the properties of an integer quantum Hall effect state at filling factor one of the lowest Landau level in presence of an anisotropic Coulomb interaction potential. We adopt a
Algebraic approach to fractional quantum Hall effect
We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaux with filling factor $\nu=N/(2N+1)$ in the large $N$ limit. By analyzing the algebra
Non relativistic diffeomorphism and the geometry of the fractional quantum Hall effect
We show that our recently proposed method\cite{BMM1,BMM2,BMM3,BM4} of constructing nonrelativistic diffeomorphism invariant field theories by gauging the Galilean symmetry provides a natural
Investigating Anisotropic Quantum Hall States with Bimetric Geometry.
A low energy effective theory of anisotropic fractional quantum Hall (FQH) states is constructed and a relationship between the shift, the Hall viscosity, and a new quantized coupling to anisotropy is derived, which is term anisospin.
Geometry of random potentials: Induction of two-dimensional gravity in quantum Hall plateau transitions
Integer quantum Hall plateau transitions are usually modeled by a system of noninteracting electrons moving in a random potential. The physics of the most relevant degrees of freedom, the edge