[Show abstract][Hide abstract] ABSTRACT: We show that the entanglement spectrum associated with a certain class of
strongly correlated many-body states --- the wave functions proposed by
Laughlin and Jain to describe the fractional quantum Hall effect --- can be
very well described in terms of a simple model of non-interacting (or weakly
interacting) composite fermions.
Physical Review B 06/2015; 92(11). DOI:10.1103/PhysRevB.92.115155 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the entanglement spectra of many particle systems in states which
are closely related to products of Slater determinants or products of
permanents, or combinations of the two. Such states notably include the
Laughlin and Jain composite fermion states which describe most of the observed
conductance plateaus of the fractional quantum Hall effect. We identify a set
of 'Entanglement Wave Functions' (EWF), for subsets of the particles, which
completely describe the entanglement spectra of such product wave functions,
both in real space and in particle space. A subset of the EWF for the Laughlin
and Jain states can be recognized as Composite Fermion states. These states
provide an exact description of the low angular momentum sectors of the real
space entanglement spectrum (RSES) of these trial wave functions and a physical
explanation of the branches of excitations observed in the RSES of the Jain
states.
Physical Review B 05/2013; 88(15). DOI:10.1103/PhysRevB.88.155307 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We devise a way to calculate the dimensions of symmetry sectors appearing in
the Particle Entanglement Spectrum (PES) and Real Space Entanglement Spectrum
(RSES) of multi-particle systems from their real space wave functions. We first
note that these ranks in the entanglement spectra equal the dimensions of
spaces of wave functions with a number of particles fixed. This also yields
equality of the multiplicities in the PES and the RSES. Our technique allows
numerical calculations for much larger systems than were previously feasible.
For somewhat smaller systems, we can find approximate entanglement energies as
well as multiplicities. We illustrate the method with results on the RSES and
PES multiplicities for integer quantum Hall states, Laughlin and Jain composite
fermion states and for the Moore-Read state at filling $\nu=5/2$, for system
sizes up to 70 particles.
[Show abstract][Hide abstract] ABSTRACT: We propose trial wave functions for quasiparticle and exciton excitations of
the Moore-Read Pfaffian fractional quantum Hall states, both for bosons and for
fermions, and study these numerically. Our construction of trial wave functions
employs a picture of the bosonic Moore-Read state as a symmetrized double layer
composite fermion state. We obtain the number of independent angular momentum
multiplets of quasiparticle and exciton trial states for systems of up to 20
electrons. We find that the counting for quasielectrons at large angular
momentum on the sphere matches that expected from the CFT which describes the
Moore-Read state's boundary theory. In particular, the counting for
quasielectrons is the same as for quasiholes, in accordance with the idea that
the CFT describing both sides of the FQH plateau should be the same. We also
show that our trial wave functions have good overlaps with exact wave functions
obtained using various interactions, including second Landau level Coulomb
interactions and the 3-body delta interaction for which the Pfaffian states and
their quasiholes are exact ground states. We discuss how these results relate
to recent work by Sreejith et al. on a similar set of trial wave functions for
excitations over the Pfaffian state as well as to earlier work by Hansson et
al., which has produced trial wave functions for quasiparticles based on
conformal field theory methods and by Bernevig and Haldane, which produced
trial wave functions based on clustering properties and `squeezing'.
[Show abstract][Hide abstract] ABSTRACT: The entanglement entropy of the integer Quantum Hall states satisfies the
area law for smooth domains with a vanishing topological term. In this paper we
consider polygonal domains for which the area law acquires a constant term that
only depends on the angles of the vertices and we give a general expression for
it. We study also the dependence of the entanglement spectrum on the geometry
and give it a simple physical interpretation.
Journal of Statistical Mechanics Theory and Experiment 07/2010; 12(12). DOI:10.1088/1742-5468/2010/12/P12033 · 2.40 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We compute the entanglement entropy, in real space, of the ground state of
the integer Quantum Hall states for three different domains embedded in the
torus, the disk and the sphere. We establish the validity of the area law with
a vanishing value of the topological entanglement entropy. The entropy per unit
length of the perimeter depends on the filling fraction, but it is independent
of the geometry.