Related papers: Exactly Solvable Hamiltonian for Non-Abelian Quasi…
We study fractional quantum Hall states in the cylinder geometry with open boundaries. By truncating the Coulomb interactions between electrons we show that it is possible to construct infinitely many exact eigenstates including the ground…
Some models of the 5/2 fractional quantum Hall state predict that the quasi-particles, which carry the charge, have non-Abelian statistics: exchange of two quasi-particles changes the wave function more dramatically than just the usual…
Exactly solvable Hamiltonians with spin liquid ground states have proven to be extremely useful, not only because they unambiguously demonstrate that these phases can arise in systems of interacting spins but also as a pedagogical…
Fibonacci anyons provide the simplest possible model of non-Abelian fusion rules: [1] x [1] = [0] + [1]. We propose a conformal field theory construction of topological quantum registers based on Fibonacci anyons realized as quasiparticle…
Composite fermions in a partially filled quasi-Landau level may be viewed as quasielectrons of the underlying fractional quantum Hall state, suggesting that a quasielectron is simply a dressed electron, as often is true in other interacting…
The current proposals for producing non-Abelian anyons and Majorana particles, which are neither fermions nor bosons, are primarily based on the realization of topological superconductivity in two dimensions. We show theoretically that the…
We study excitations in edge theories for non-abelian quantum Hall states, focussing on the spin polarized states proposed by Read and Rezayi and on the spin singlet states proposed by two of the authors. By studying the exclusion…
The study of quantum quasi-particles at low temperatures including their statistics, is a frontier area in modern physics. In a seminal paper F.D. Haldane proposed a definition based on a generalization of the Pauli exclusion principle for…
We analyze the effect of exchanging quasiholes described by Gaffnian quantum Hall trial state wave functions. This exchange is carried out via adiabatic transport using the recently developed coherent state Ansatz. We argue that our Ansatz…
Analytical calculations based on a Landau Level (LL) picture are reported for a many-electron system moving in an interface (with a finite-width Quantum Well (QW)) and in the presence of an external perpendicular magnetic field. They lead…
A powerful approach to solve the Coulombic quantum three-body problem is proposed. The approach is exponentially convergent and more efficient than the Hyperspherical Coordinate(HC) method and the Correlation Function Hyperspherical…
In the hierarchical theory of the fractional quantum Hall effect, the low--energy behaviour of a daughter state in the next level of the hierarchy is described by an interacting system of quasiparticles of the parent state. Taking the…
We study a pairing mechanism for the quantum Hall system using a mean field theory with a basis on the von Neumann lattice, on which the magnetic translations commute. In the Hartree-Fock-Bogoliubov approximation, we solve the gap equation…
We consider a two dimensional (2D) model of particles interacting in a Landau level. We work in a finite disk geometry and take the particles to interact with a linearly decreasing two-body Haldane pseudo-potential. We show that the ground…
The quasiparticles (QPs) or quasiholes (QHs) of fractional quantum Hall states have been predicted to obey fractional braid statistics, which refers to the Berry phase (in addition to the usual Aharonov-Bohm phase) associated with an…
We determine the exclusion statistics properties of the fundamental edge quasi-particles over a specific $\nu=\half$ non-abelian quantum Hall state known as the pfaffian. The fundamental excitations are the edge electrons of charge $-e$ and…
Choosing an appropriate representation of the molecular Hamiltonian is one of the challenges faced by simulations of the nonadiabatic quantum dynamics around a conical intersection. The adiabatic, exact quasidiabatic, and strictly diabatic…
We introduce a new renormalisation scheme to construct the Landau quasiparticles of Fermi fluids. The scheme relies on an energy cutoff $\Lambda$ which removes the quasi-resonant couplings, enabling the dressing of the particles into…
We construct a class of exact eigenstates of the Hamiltonian obtained by projecting the Hubbard interaction term onto the flat band subspace of a generic lattice model. These exact eigenstates are many body states in which an arbitrary…
Starting from a one-particle quasi-exactly solvable system, which is characterized by an intrinsic sl(2) algebraic structure and the energy-reflection symmetry, we construct a daughter N-body Hamiltonian presenting a deformation of the…