THE GROUND STATE STRUCTURE AND MODULAR TRANSFORMATIONS OF FRACTIONAL QUANTUM HALL STATES ON A TORUS

1993/03/31 by Esko Keski-Vakkuri, ESKO KESKI-VAKKURI, Xiao-Gang Wen +1 · 10 citations
Materials Science · Physics and Astronomy · #Conformal field theory #Degeneracy (biology) #Fractional quantum Hall effect #Ground state #Quantum Hall effect #Quantum and electron transport phenomena #Quantum spin Hall effect #Quasicrystal Structures and Properties #Singlet state #Topological Materials and Phenomena #Torus #Wave function #hep-th

paper · pdf · doi:10.1142/s0217979293003644

published as Int. J. Mod. Phys. B7 (1993) 4227-4260 · 28 pages, LATEX, 9 figures available by request from authors, CTP-2197 (two references added + some minor typos corrected)

arxiv created 1993/06/06 · openalex publication_date 1993/11/15 · arxiv updated 2009/11/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05

Abstract

The structure of ground states of generic FQH states on a torus is studied by using both effective theory and electron wavefunction. The relation between the effective theory and the wavefunction becomes transparent when one considers the ground state structure. We find that the non-abelian Berry’s phases of the abelian Hall states generated by twisting the mass matrix are identical to the modular transformation matrix for the characters of Gaussian conformal field theory. We also show that the Haldane-Rezayi spin singlet state has a ten fold ground state degeneracy on a torus which indicates such a state is a non-abelian Hall state.

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