1997/11/30 by Xiao-Gang Wen, X. G. Wen, A. Zee · 3 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevb.58.15717
published as Phys.Rev. B58 (1998) 15717 · 33 pages, LaTeX+epsf, 2 eps figures. Expanded version
arxiv created 1998/08/25 · openalex publication_date 1998/12/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a simple approach to calculate the degeneracy and the structure of the ground states of non-Abelian quantum Hall (QH) liquids on the torus. Our approach can be applied to any QH liquids (Abelian or non-Abelian) obtained from the parton construction. We explain our approach by studying a series of examples of increasing complexity. When the effective theory of a non-Abelian QH liquid is a non-Abelian Chern-Simons (CS) theory, our approach reproduces the well-known results for the ground-state degeneracy of the CS theory. However, our approach also applies to non-Abelian QH liquids whose effective theories are not known and which cannot be written as a non-Abelian CS theory. We find that the ground states on a torus of all non-Abelian QH liquids obtained from the parton construction can be described by points on a lattice inside a ``folded unit cell.'' The folding is generated by reflection, rotations, etc. Thus the ground-state structures on the torus described by the ``folded unit cells'' provide a way to (at least partially) classify non-Abelian QH liquids obtained from the parton construction.