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SUMMARY:The complete solution of the quartic analogue of the Kontsevich mo
del
DTSTART;VALUE=DATE-TIME:20200619T120000Z
DTEND;VALUE=DATE-TIME:20200619T130000Z
DTSTAMP;VALUE=DATE-TIME:20200713T111600Z
UID:indico-event-5848@indico.math.cnrs.fr
DESCRIPTION:Speakers: Raimar Wulkenhaar\nWe consider an analogue of Kontse
vich's matrix Airy function where the cubic potential $\\mathrm{Tr}(\\Phi^
3)$ is replaced by a quartic term $\\mathrm{Tr}(\\Phi^4)$. We show that\,
for finite matrices\, all cumulants are exactly solvable in terms rational
functions\, their branch points and their inverses. For the planar sector
we also control the limit to infinite matrices where generating functions
of hyperlogarithms are produced.\nhttps://indico.math.cnrs.fr/event/5848/
LOCATION:Zoom (Institut Camille Jordan)
URL:https://indico.math.cnrs.fr/event/5848/
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SUMMARY:Spin textures in quantum Hall ferromagnets
DTSTART;VALUE=DATE-TIME:20200626T120000Z
DTEND;VALUE=DATE-TIME:20200626T130000Z
DTSTAMP;VALUE=DATE-TIME:20200713T111600Z
UID:indico-event-5865@indico.math.cnrs.fr
DESCRIPTION:Speakers: Benoit Douçot\nIn the presence of a strong magnetic
field\, and for an integer filling\nof the Landau levels\, Coulomb intera
ctions favor a ferromagnetic ground-state.\nIt has been shown already twen
ty years ago\, both theoretically and experimentally\,\nthat when extra ch
arges are added or removed to such systems\,\nthe ferromagnetic state beco
mes unstable and is replaced\nby spin textures called Skyrmions. We have g
eneralized this notion to an arbitrary\nnumber d of internal states for th
e electrons\, which may correspond to the combination\nof spin\, valley\,
or layer indices.\nThe first step is to associate a many electron wave-fun
ction\, projected on the\nlowest Landau level\, to any classical spin text
ure described by a smooth map from the plane\nto the projective space CP(d
-1). In the large magnetic field limit\, we assume that the spin texture\n
is slowly varying on the scale of the magnetic length\, which allows us\nt
o evaluate the expectation value of the interaction Hamiltonian on these m
any electron quantum states.\nThe first non trivial term in this semi-clas
sical expansion is the usual CP(d-1) non-linear sigma model\,\nwhich is kn
own to exhibit a remarkable degeneracy of the many electron states obtaine
d from holomorphic\ntextures. Surprisingly\, this degeneracy is not lifted
by reintroducing quantum fluctuations.\nIt is eventually lifted by the su
b-leading term in the effective Hamiltonian\, which\nselects a hexagonal S
kyrmion lattice and therefore breaks both translational and internal SU(d)
symmetries.\nI will show that these optimal classical textures can be int
erpreted in\nan appealing way using geometric quantization.\nhttps://indic
o.math.cnrs.fr/event/5865/
LOCATION:Zoom (Institut Camille Jordan)
URL:https://indico.math.cnrs.fr/event/5865/
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