Some properties of Grassmannian $U(4)/U(2{)}^2$ coherent states and an entropic conjecture

Abstract

We analyze mathematical and physical properties of a previously introduced [J. Phys. A47, 115302 (2014)] family of $U(4)$ coherent states (CS). They constitute a matrix version of standard spin $U(2)$ CS when we add an extra (pseudospin) dichotomous degree of freedom: layer, sublattice, two-well, nucleon, etc. Applications to bilayer quantum Hall systems at fractions of filling factor $\nu =2$ are discussed, where Haldane's sphere picture is generalized to a Grassmannian picture. We also extend Wehrl's definition of entropy from Glauber to Grassmannian CS and state a conjecture on the entropy lower bound.

17 pages, 1 figure. Minor changes

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Cited by in corpus (3)

• Hilbert space and ground state structure of bilayer quantum Hall systems at $\nu =2/\lambda$
• Hilbert space structure of the low energy sector of U(N) quantum Hall ferromagnets and their classical limit
• Husimi function and phase-space analysis of bilayer quantum Hall systems at $\nu =2/\lambda$