相关论文: Exactly Solvable Hamiltonian for Non-Abelian Quasi…
The Pfaffian state is an attractive candidate for the observed quantized Hall plateau at Landau level filling fraction $\nu=5/2$. This is particularly intriguing because this state has unusual topological properties, including quasiparticle…
The quasiparticles in Quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could in principle be used for…
Wave functions describing quasiholes and electrons in nonabelian quantum Hall states are well known to correspond to conformal blocks of certain coset conformal field theories. In this paper we explicitly analyse the algebraic structure…
We further develop an approach to identify the braiding statistics associated to a given fractional quantum Hall state through adiabatic transport of quasiparticles. This approach is based on the notion of adiabatic continuity between…
Exactly solvable models of topologically ordered phases with non-abelian anyons typically require complicated many-body interactions which do not naturally appear in nature. This motivates the "inverse problem" of quantum many-body physics:…
We construct a class of lattice Hamiltonians whose single-particle spectrum consists of an arbitrary number of exactly degenerate flat bands that reproduce the analytic structure of the first $p$ Landau levels restricted to the lattice.…
The quasihole states of several paired states, the Pfaffian, Haldane-Rezayi, and 331 states, which under certain conditions may describe electrons at filling factor $\nu=1/2$ or 5/2, are studied, analytically and numerically, in the…
We have tested Haldane's ``fractional-Pauli-principle'' description of excitations around the $\nu = 1/3$ state in the FQHE, using exact results for small systems of electrons. We find that Haldane's prediction $\beta = \pm 1/m$ for…
We derive effective Hamiltonians for the fractional quantum Hall effect in n=0 and n=1 Landau levels that account perturbatively for Landau level mixing by electron-electron interactions. To second order in the ratio of electron-electron…
We construct a series of 2+1-dimensional models whose quasiparticles obey non-Abelian statistics. The adiabatic transport of quasiparticles is described by using a correspondence between the braid matrix of the particles and the scattering…
The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular nonabelian ones.…
The observed fractional quantum Hall (FQH) plateaus follow a recurring hierarchical structure that allows an understanding of complex states based on simpler ones. Condensing the elementary quasiparticles of an Abelian FQH state results in…
Fractional quantum Hall (FQH) states host fractionally charged anyons with exotic exchange statistics. Of particular interest are FQH phases supporting non-Abelian anyons, which can encode topologically protected quantum information. In…
On a nonrelativistic contact four-fermion model we have shown that the simple Lambda-cut-off prescription together with definite fine-tuning of the Lambda dependency of "bare"quantities lead to self-adjoint semi-bounded Hamiltonian in one-,…
An important development in the field of the fractional quantum Hall effect has been the proposal that the 5/2 state observed in the Landau level with orbital index $n = 1$ of two dimensional electrons in a GaAs quantum well originates from…
Cumrun Vafa proposed a new unifying model for the principal series of FQHE which predicts non-Abelian statistics of the quasi-holes. The many-body Hamiltonian supporting these topological phases of matter is invariant under four…
Topological quantum information processing relies on adiabatic braiding of nonabelian quasiparticles. Performing the braiding operations in finite time introduces transitions out of the ground-state manifold and deviations from the…
We report on our systematic attempts at finding local interactions for which the lowest-Landau-level projected composite-fermion wave functions are the unique zero energy ground states. For this purpose, we study in detail the simplest…
We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level, most notably the one at filling fraction…
We demonstrate how to directly study non-Abelian statistics for a wide class of exactly solvable many-body quantum systems. By employing exact eigenstates to simulate the adiabatic transport of a model's quasiparticles, the resulting Berry…