arXiv subjects

E. H. Rezayi

Publications and source records attributed to E. H. Rezayi.

At least 37 records · Page 2Linked to original sources

arXiv2008

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

We present a comprehensive numerical study of a microscopic model of the fractional quantum Hall system at filling fraction $ν= 5/2$, based on the disc geometry. Our model includes Coulomb interaction and a semi-realistic confining potential. We also mix in some three-body interaction in some cases to help elucidate the physics. We obtain a phase diagram, discuss the conditions under which the ground state can be described by the Moore-Read state, and study its competition with neighboring stripe phases. We also study quasihole excitations and edge excitations in the Moore-Read--like state. From the evolution of edge spectrum, we obtain the velocities of the charge and neutral edge modes, which turn out to be very different. This separation of velocities is a source of decoherence for a non-Abelian quasihole/quasiparticle (with charge $\pm e/4$) when propagating at the edge; using numbers obtained from a specific set of parameters we estimate the decoherence length to be around four microns. This sets an upper bound for the separation of the two point contacts in a double point contact interferometer, designed to detect the non-Abelian nature of such quasiparticles. We also find a state that is a potential candidate for the recently proposed anti-Pfaffian state. We find the speculated anti-Pfaffian state is favored in weak confinement (smooth edge) while the Moore-Read Pfaffian state is favored in strong confinement (sharp edge).

cond-mat.mes-hall↗

arXiv2007

Bipartite entanglement entropy in fractional quantum Hall states

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 of a FQH state can be extracted from wavefunctions for a limited number of particles.

cond-mat.mes-hall↗

arXiv2007

Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime

In fractional quantum Hall physics, the Hilbert space is projected to a single Landau level and the entire Hamiltonian consists of just the projected inter-electron interaction. Haldane's pseudopotential formalism has been an extremely useful tool both for understanding these interactions, and for understanding the quantum Hall states that result. In the current paper we consider the analogue of this pseudopotential construction that results from general M-body interactions rather than the usual (Coulomb) two-body interaction.

cond-mat.mes-hall↗

arXiv2007

Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement

We study the ground state and low-energy excitations of fractional quantum Hall systems on a disk at filling fraction $ν= 5/2$, with Coulomb interaction and background confining potential. We find the Moore-Read ground state is stable within a finite but narrow window in parameter space. The corresponding low-energy excitations contain a fermionic branch and a bosonic branch, with widely different velocities. A short-range repulsive potential can stabilize a charge $+e/4$ quasihole at the center, leading to a different edge excitation spectrum due to the change of boundary conditions for Majorana fermions, clearly indicating the non-Abelian nature of the quasihole.

cond-mat.mes-hall↗

arXiv2006

Competing Compressible and Incompressible Phases in Rotating Atomic Bose Gases at Filling Factor $ν=2$

We study the groundstates of weakly interacting atomic Bose gases under conditions of rapid rotation. We present the results of large-scale exact diagonalisation studies on a periodic geometry (a torus) which allows studies of compressible states with broken translational symmetry. Focusing on filling factor $ν=2$, we show a competition between the triangular vortex lattice, a quantum smectic state, and the incompressible $k=4$ Read-Rezayi state. We discuss the corrections arising from finite size effects, and the likely behaviour for large system sizes. The Read-Rezayi state is stabilised by a moderate amount of additional dipolar interactions.

cond-mat.mes-hall↗

arXiv2006

A nu=2/5 Paired Wavefunction

We construct a wavefunction, generalizing the well known Moore-Read Pfaffian, that describes spinless electrons at filling fraction nu=2/5 (or bosons at filling fraction nu=2/3) as the ground state of a very simple three body potential. We find, analogous to the Pfaffian, that when quasiholes are added there is a ground state degeneracy which can be identified as zero-modes of the quasiholes. The zero-modes are identified as having semionic statistics. We write this wavefunction as a correlator of the Virasoro minimal model conformal field theory M(5,3). Since this model is non-unitary, we conclude that this wavefunction is a quantum critical state. Nonetheless, we find that the overlaps of this wavefunction with exact diagonalizations in the lowest and first excited Landau level are very high, suggesting that this wavefunction may have experimental relevance for some transition that may occur in that regime.

cond-mat.mes-hall↗

arXiv2006

Generalized Quantum Hall Projection Hamiltonians

Certain well known quantum Hall states -- including the Laughlin states, the Moore-Read Pfaffian, and the Read-Rezayi Parafermion states -- can be defined as the unique lowest degree symmetric analytic function that vanishes as at least p powers as some number (g+1) of particles approach the same point. Analogously, these same quantum Hall states can be generated as the exact highest density zero energy state of simple angular momentum projection operators. Following this theme we determine the highest density zero energy state for many other values of p and g.

cond-mat.mes-hall↗

arXiv2006

Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level

We present results of extensive numerical calculations on the ground state of electrons in the first excited (n=1) Landau level with Coulomb interactions, and including non-zero thickness effects, for filling factors 12/5 and 13/5 in the torus geometry. In a region that includes these experimentally-relevant values, we find that the energy spectrum and the overlaps with the trial states support the previous hypothesis that the system is in the non-Abelian k = 3 liquid phase we introduced in a previous paper.

cond-mat.mes-hall↗

arXiv2005

Incompressible liquid state of rapidly-rotating bosons at filling factor 3/2

Bosons in the lowest Landau level, such as rapidly-rotating cold trapped atoms, are investigated numerically in the specially interesting case in which the filling factor (ratio of particle number to vortex number) is 3/2. When a moderate amount of a longer-range (e.g. dipolar) interaction is included, we find clear evidence that the ground state is in a phase constructed earlier by two of us, in which excitations possess non-Abelian statistics.

cond-mat.mes-hall↗

arXiv2005

Vortex Lattices in Rotating Atomic Bose Gases with Dipolar Interactions

We show that dipolar interactions have dramatic effects on the groundstates of rotating atomic Bose gases in the weak interaction limit. With increasing dipolar interaction (relative to the net contact interaction), the mean-field, or high filling fraction, groundstate undergoes a series of transitions between vortex lattices of different symmetries: triangular, square, ``stripe'', and ``bubble'' phases. We also study the effects of dipolar interactions on the quantum fluids at low filling fractions. We show that the incompressible Laughlin state at filling fraction $ν=1/2$ is replaced by compressible stripe and bubble phases.

cond-mat.mes-hall↗

arXiv2005

Mobility gap in fractional quantum Hall liquids: Effects of disorder and layer thickness

We study the behavior of two-dimensional electron gas in the fractional quantum Hall regime in the presence of finite layer thickness and correlated disordered potential. Generalizing the Chern number calculation to many-body systems, we determine the mobility gaps of fractional quantum Hall states based on the distribution of Chern numbers in a microscopic model. We find excellent agreement between experimentally measured activation gaps and our calculated mobility gaps, when combining the effects of both disordered potential and layer thickness. We clarify the difference between mobility gap and spectral gap of fractional quantum Hall states and explain the disorder-driven collapse of the gap and the subsequent transitions from the fractional quantum Hall states to insulator.

cond-mat.mes-hall↗

arXiv2004

Universality of the edge tunneling exponent of fractional quantum Hall liquids

Recent calculations of the edge tunneling exponents in quantum Hall states appear to contradict their topological nature. We revisit this issue and find no fundamental discrepancies. In a microscopic model of fractional quantum Hall liquids with electron-electron interaction and confinement, we calculate the edge Green's function via exact diagonalization. Our results for $ν= 1/3$ and 2/3 suggest that in the presence of Coulomb interaction, the sharpness of the edge and the strength of the edge confining potential, which can lead to edge reconstruction, are the parameters that are relevant to the universality of the electron tunneling I-V exponent.

cond-mat.mes-hall↗

arXiv2003

Disorder driven collapse of the mobility gap and transition to an insulator in fractional quantum Hall effect

We study the nu=1/3 quantum Hall state in presence of the random disorder. We calculate the topologically invariant Chern number, which is the only quantity known at present to unambiguously distinguish between insulating and current carrying states in an interacting system. The mobility gap can be determined numerically this way, which is found to agree with experimental value semiquantitatively. As the disorder strength increases towards a critical value, both the mobility gap and plateau width narrow continuously and ultimately collapse leading to an insulating phase.

cond-mat.mes-hall↗

arXiv2003

Edge reconstruction in the fractional quantum Hall regime

The interplay of electron-electron interaction and confining potential can lead to the reconstruction of fractional quantum Hall edges. We have performed exact diagonalization studies on microscopic models of fractional quantum Hall liquids, in finite size systems with disk geometry, and found numerical evidence of edge reconstruction under rather general conditions. In the present work we have taken into account effects like layer thickness and Landau level mixing, which are found to be of quantitative importance in edge physics. Due to edge reconstruction, additional nonchiral edge modes arise for both incompressible and compressible states. These additional modes couple to electromagnetic fields and thus can be detected in microwave conductivity measurements. They are also expected to affect the exponent of electron Green's function, which has been measured in tunneling experiments. We have studied in this work the electric dipole spectral function that is directly related to the microwave conductivity measurement. Our results are consistent with the enhanced microwave conductivity observed in experiments performed on samples with an array of antidots at low temperatures, and its suppression at higher temperatures. We also discuss the effects of the edge reconstruction on the single electron spectral function at the edge.

cond-mat.mes-hall↗

arXiv2003

Exact diagonalization study of domain structure in integer filling factor quantum Hall ferromagnets

Opposite spin Landau levels in a quantum well can be brought into coincidence by tilting the magnetic field away from normal orientation. We demonstrate that the magnetotransport anomaly at integer filling factors that was recently discovered by Pan {\it et al} is due to such a coincidence. By performing exact diagonalization calculations using microscopically evaluated effective electron-electron interactions, we are able to establish that the electronic ground state at coincidence is an Ising quantum Hall ferromagnet and that the low energy excitations correspond to the formation of a domain wall.

cond-mat.mes-hall↗

arXiv2003

Coexistence of Composite-Bosons and Composite-Fermions in nu=1/2 + 1/2 Quantum Hall Bilayers

In bilayer quantum Hall systems at filling fractions near nu=1/2+1/2, as the spacing d between the layers is continuously decreased, intra-layer correlations must be replaced by inter-layer correlations, and the composite fermion (CF) Fermi seas at large d must eventually be replaced by a composite boson (CB) condensate or "111 state" at small d. We propose a scenario where CBs and CFs coexist in two interpenetrating fluids in the transition. Trial wavefunctions describing these mixed CB-CF states compare very favorably with exact diagonalization results. A Chern-Simons transport theory is constructed that is compatible with experiment.

cond-mat.mes-hall↗

arXiv2002

Possible Pairing-Induced Even-Denominator Fractional Quantum Hall Effect in the Lowest Landau Level

We report on our theoretical investigations that point to the possibility of a fractional quantum Hall effect with partial spin polarization at $ν=3/8$. The physics of the incompressible state proposed here involves p-wave pairing of composite fermions in the spin reversed sector. The temperature and magnetic field regimes for the realization of this state are estimated.

cond-mat.mes-hall↗

arXiv2002

Reconstruction of Fractional Quantum Hall Edges

We study the interplay of interaction, confining potential and effects of finite temperature at the edge of a quantum Hall liquid. Our exact diagonalization calculation indicates that edge reconstruction occurs in the fractional quantum Hall regime for a variety of confining potential, including ones that correspond to a "sharp" edge. Our finite temperature Hartree-Fock calculation for integer quantum Hall edges indicates that reconstruction is suppressed above certain temperature. We discuss the implication of our results on recent edge tunneling and microwave absorption experiments.

cond-mat.mes-hall↗