233 research outputs found
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.Comment: 5 pages (Revtex4), 7 figure
Entanglement entropy of the composite fermion non-Fermi liquid state
The so-called ``non-Fermi liquid'' behavior is very common in strongly
correlated systems. However, its operational definition in terms of ``what it
is not'' is a major obstacle against theoretical understanding of this
fascinating correlated state. Recently there has been much interest in
entanglement entropy as a theoretical tool to study non-Fermi liquids. So far
explicit calculations have been limited to models without direct experimental
realizations. Here we focus on a two dimensional electron fluid under magnetic
field and filling fraction , which is believed to be a non-Fermi
liquid state. Using the composite fermion (CF) wave-function which captures the
state very accurately, we compute the second R\'enyi entropy using
variational Monte-Carlo technique and an efficient parallel algorithm. We find
the entanglement entropy scales as with the length of the boundary
as it does for free fermions, albeit with a pre-factor twice that of the
free fermion. We contrast the results against theoretical conjectures and
discuss the implications of the results.Comment: 4+ page
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.Comment: Replaced with the published version which has a new title and some
other chage
Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian 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 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 for the Pfaffian, 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 there's more.Comment: 43 pages, requires RevTeX. The 14 figures and 2 tables are available
on request at [email protected] (include mailing address
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.Comment: 12 pages, 7 figures, small corrections to table III and references
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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.Comment: 4 pages with 4 figure
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