Prof. Duncan Haldan delivers seminar on Monday

[Cond.Matt. & Stat.Mech.Section]

JOINT ICTP/SISSA CONDENSED MATTER SEMINAR

 

Monday, 4 June    -    4:00 p.m.

 

Luigi Stasi Seminar Room,  ICTP Leonardo Building (1st floor)

  

F.D.M. HALDANE     ( Princeton University )

 

" Geometry and incompressibility in the fractional quantum Hall effect"

  

Abstract

 

 Incompressibility in the fractional QHE is identified as a variant of Mott-Hubbard incompressibility, where additional electrons are excluded from a region occupied by a “composite boson” of p electrons in q orbitals (or p electrons with q “attached flux quanta”) at Landau-level filling \nu = p/q. The new ingredient is that the shape of this “exclusion zone” is described by an intrinsic ”unimodular” (determinant = 1) spatial metric tensor field g_{ab}(x,t), that is a true dynamical variable that fluctuates about the shape that minimizes the correlation energy of the FQH state. It emerges that the electron density is pinned to the combination peB-\hbar s K_g  rather than to the magnetic flux density B alone, where K_g is the gaussian curvature of the metric, and s is a new characteristic topologically-quantized ”guiding-center spin” related to the so-called ”shift” of the FQH state. This metric can be seen in the Laughlin state as a explicit variational parameter that has remained hidden for the past thirty years because of a fundamental misinterpretation of the Laughlin state as a ”lowest Landau level Schrödinger wavefunction”: (in fact it is a guiding-center coherent state that does not depend on which Landau level is partially filled).