E. H. Rezayi

Incompressible paired hall state, stripe order, and the composite fermion liquid phase in half-filled landau levels

We consider the two lowest Landau levels at half filling. In the higher Landau level (nu = 5/2), we find a first-order phase transition separating a compressible striped phase from a paired quantum Hall state, which is identified as the Moore-Read state. The critical point is very near the Coulomb potential and the transition can be driven by increasing the width of the electron layer. We find a much weaker transition (either second-order or a crossover) from pairing to the composite fermion Fermi-liquid behavior. A very similar picture is obtained for the lowest Landau level, but the transition point is not near the Coulomb potential.

Quasiholes and fermionic zero modes of paired fractional quantum Hall states: The mechanism for non-Abelian statistics

The quasihole states of several paired states, the Pfaffian, Haldane-Rezayi, and 331 states, which under certain conditions may describe electrons at filling factor

Bipartite entanglement entropy in fractional quantum Hall states

\nu=1/2

Infinite density matrix renormalization group for multicomponent quantum Hall systems

or 5/2, are studied, analytically and numerically, in the spherical geometry, for the Hamiltonians for which the ground states are known exactly. We also find all the ground states (without quasiparticles) of these systems in the toroidal geometry. In each case, a complete set of linearly-independent functions that are energy eigenstates of zero energy is found explicitly. For fixed positions of the quasiholes, the number of linearly-independent states is

Incompressible Liquid State of Rapidly Rotating Bosons at Filling Factor 3 / 2

2^{n-1}

Edge state inner products and real-space entanglement spectrum of trial quantum Hall states

for the Pfaffian,

Real-space entanglement spectrum of quantum Hall systems

2^{2n-3}

Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States

for the Haldane-Rezayi state; these degeneracies are needed if these systems are to possess nonabelian statistics, and they agree with predictions based on conformal field theory. The dimensions of the spaces of states for each number of quasiholes agree with numerical results for moderate system sizes. The effects of tunneling and of the Zeeman term are discussed for the 331 and Haldane-Rezayi states, as well as the relation to Laughlin states of electron pairs. A model introduced by Ho, which was supposed to connect the 331 and Pfaffian states, is found to have the same degeneracies of zero-energy states as the 331 state, except at its Pfaffian point where it is much more highly degenerate than either the 331 or the Pfaffian. We introduce a modification of the model which has the degeneracies of the 331 state everywhere including the Pfaffian point; at the latter point, tunneling reduces the degeneracies to those of the Pfaffian state. An experimental difference is pointed out between the Laughlin states of electron pairs and the other paired states, in the current-voltage response when electrons tunnel into the edge. And theres more.

Fractional quantum Hall effect at ν = 5 ∕ 2 : Ground states, non-Abelian quasiholes, and edge modes in a microscopic model

We present a detailed analysis of bipartite entanglement entropies in fractional quantum Hall (FQH) states, considering both Abelian (Laughlin) and non-Abelian (Moore-Read) states. We derive upper bounds for the entanglement between two subsets of the particles making up the state. We also consider the entanglement between spatial regions supporting a FQH state. Using the latter, we show how the so-called topological entanglement entropy

Trial wave functions for ν = 1 2 + 1 2 quantum Hall bilayers

\ensuremath{\gamma}