Berry Phase and Model Wave Function in the Half-Filled Landau Level.

We construct model wave functions for the half-filled Landau level parametrized by "composite fermion occupation-number configurations" in a two-dimensional momentum space, which correspond to a Fermi sea with particle-hole excitations. When these correspond to a weakly excited Fermi sea, they have a large overlap with wave functions obtained by the exact diagonalization of lowest-Landau-level electrons interacting with a Coulomb interaction, allowing exact states to be identified with quasiparticle configurations. We then formulate a many-body version of the single-particle Berry phase for adiabatic transport of a single quasiparticle around a path in momentum space, and evaluate it using a sequence of exact eigenstates in which a single quasiparticle moves incrementally. In this formulation the standard free-particle construction in terms of the overlap between "periodic parts of successive Bloch wave functions" is reinterpreted as the matrix element of a "momentum boost" operator between the full Bloch states, which becomes the matrix elements of a Girvin-MacDonald-Platzman density operator in the many-body context. This allows the computation of the Berry phase for the transport of a single composite fermion around the Fermi surface. In addition to a phase contributed by the density operator, we find a phase of exactly π for this process.

Publisher's Note: Investigating Anisotropic Quantum Hall States with Bimetric Geometry [Phys. Rev. Lett. 119, 146602 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.119.146602.

Publisher's Note: Investigating Anisotropic Quantum Hall States with Bimetric Geometry [Phys. Rev. Lett. 119, 146602 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.119.146602.

Investigating Anisotropic Quantum Hall States with Bimetric Geometry.

We construct a low energy effective theory of anisotropic fractional quantum Hall (FQH) states. We develop a formalism similar to that used in the bimetric approach to massive gravity, and apply it to describe Abelian anisotropic FQH states in the presence of external electromagnetic and geometric backgrounds. We derive a relationship between the shift, the Hall viscosity, and a new quantized coupling to anisotropy, which we term anisospin. We verify this relationship by numerically computing the Hall viscosity for a variety of anisotropic quantum Hall states using the density matrix renormalization group. Finally, we apply these techniques to the problem of nematic order and clarify certain disagreements that exist in the literature about the meaning of the coefficient of the Berry phase term in the nematic effective action.

The half-filled Landau level: The case for Dirac composite fermions.

In a two-dimensional electron gas under a strong magnetic field, correlations generate emergent excitations distinct from electrons. It has been predicted that "composite fermions"--bound states of an electron with two magnetic flux quanta--can experience zero net magnetic field and form a Fermi sea. Using infinite-cylinder density matrix renormalization group numerical simulations, we verify the existence of this exotic Fermi sea, but find that the phase exhibits particle-hole symmetry. This is self-consistent only if composite fermions are massless Dirac particles, similar to the surface of a topological insulator. Exploiting this analogy, we observe the suppression of 2k(F) backscattering, a characteristic of Dirac particles. Thus, the phenomenology of Dirac fermions is also relevant to two-dimensional electron gases in the quantum Hall regime.

Evaluation of half-life of 198Au.

The half-life of the important radioisotope (198)Au is evaluated by using several different statistical methods, such as weighted mean (WM), limitation of statistical weights method (LWM), normalized residuals method (NRM), Rajeval technique (RT), Bootstrap median (BM) and Mandel-Paule method (MP). After comparing and analyzing the results from these methods, a final value of 2.6948±0.0012d is recommended based on the stability and sensitivity of the methods and the resulting uncertainties.