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UID:1-272@lptms.universite-paris-saclay.fr
DTSTART:20140919T140000Z
DTEND:20140919T170000Z
DTSTAMP:20140909T123439Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/soutenance-de-the
 se-paul-soule/
SUMMARY:Soutenance de thèse : Paul Soulé - LPTMS-batiment 100\, salle des
  conseils - 19 Sep 14 14:00
DESCRIPTION:Edges of Fractional Quantum Hall Phases in a Cylindrical Geomet
 ry\nPaul Soulé\, LPTMS\nFractional Quantum Hall (FQH) phases are exotic i
 ncompressible fluids which support gapless chiral edge excitations. I will
  present a microscopic study of those edges states in a cylindrical geomet
 ry where quasiparticles are able to tunnel between edges.\nWe first study 
 the principal FQH phase at the filling fraction 1/3 whose ground state is 
 well described by the Laughlin wave function. For an energy scale lower th
 an the bulk gap\, the effective theory is given by a very special one dime
 nsional electron fluid localized at the edge: a chiral Luttinger liquid. U
 sing numerical exact diagonalizations\, we study the spectrum of edge mode
 s formed by the two counter-propagating edges on each side of the cylinder
 . We show that the two edges combine to form a non-chiral finite-size Lutt
 inger liquid\, where the current term reflects the transfer of quasipartic
 les between edges. Then\, we estimate numerically the Luttinger parameter 
 for a small number of particles and find it coherent with the one predicte
 d by X. G. Wen theory.\nWe then analyse edge modes of the FQH phase at fil
 ling fraction 5/2. From a Conformal Field Theory (CFT) based construction\
 , Moore and Read (Nucl. Phys. B\, 1991) proposed that this phase is well d
 escribed by a P-wave paired state of composite fermions. A striking proper
 ty of this state is that emergent excitations braid with non-abelian stati
 stics. When localized along the edge\, those excitations are described thr
 ough a chiral boson and a Majorana fermion. In the cylinder geometry\, we 
 show that the spectrum of edge excitations is composed of all conformal to
 wers of the IsingXU(1) model. Interestingly\, the non-abelian tower is nat
 urally observed as opposed to the usual disk geometry. In addition\, with 
 a Monte Carlo method\, we estimate the various scaling dimensions for larg
 e systems (about 50 electrons)\, and find them consistent with the CFT pre
 dictions.\n&nbsp\;
LOCATION:LPTMS-batiment 100\, salle des conseils\, 15 Rue Georges Clemencea
 u\, Orsay\, France
GEO:48.698200;2.181770
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=15 Rue Georges Clemenceau\,
  Orsay\, France;X-APPLE-RADIUS=100;X-TITLE=LPTMS-batiment 100\, salle des 
 conseils:geo:48.698200,2.181770
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