Publications (6)24.71 Total impact
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ABSTRACT: We show that the entanglement spectrum associated with a certain class of strongly correlated manybody 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 noninteracting (or weakly interacting) composite fermions.  [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.  [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 multiparticle 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 MooreRead 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 MooreRead 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 MooreRead 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 MooreRead 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 3body 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.  [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.
Publication Stats
83  Citations  
24.71  Total Impact Points  
Top Journals
Institutions

2015

Max Planck Institute of Quantum Optics
Arching, Bavaria, Germany


20102011

National University of Ireland, Maynooth
 Department of Mathematical Physics
Maigh Nuad, Leinster, Ireland


2008

Spanish National Research Council
Madrid, Madrid, Spain
