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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 \;
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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