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SUMMARY:Geometry and large N limits in Quantum Hall effect. - Semyon Klevt
 sov (Cologne)
DTSTART:20151118T141500Z
DTEND:20151118T151500Z
UID:TALK60137@talks.cam.ac.uk
CONTACT:Dr. J Ross
DESCRIPTION:Quantum Hall effect occurs is real-world materials and is char
 acterised by a precise quantization of Hall conductance\, which can take i
 nteger of fractional values. This phenomenon has a geometric origin and be
 st understood when considering QH states on Riemann surfaces. Main goal of
  the theory is to compute adiabatic phases corresponding to various geomet
 ric deformations (associated with the line bundle\, metric and complex str
 ucture moduli)\, in the limit of a large number of particles. I will defin
 e the objects involved\, and then give a complete solution of the problem 
 for the integer QH states and for the Laughlin states in the fractional QH
 E\, by computing the generating functional for these states. In the intege
 r QH our method relies on methods borrowed form Kahler geometry\, such as 
 Bergman kernel expansion for high powers of holomorphic line bundle\, and 
 the answer is expressed in terms of energy functionals in Kahler geometry.
  We explain the relation of geometric phases to Quillen theory of determin
 ant line bundles\, using Bismut-Gillet-Soule anomaly formulas. For the muc
 h harder Laughlin states no rigorous methods are available\, yet we still 
 can compute the generating functional by physics methods such as path inte
 gral.
LOCATION:CMS MR13
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