2005/09/30 by Alexander Seidel, Henry Fu, Dung‐Hai Lee +4 · 7 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Conservation law #Degenerate energy levels #Hamiltonian (control theory) #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Theoretical physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevlett.95.266405
published as Phys. Rev. Lett. 95, 266405 (2005) · updated version, to be published by PRL
arxiv created 2005/11/03 · openalex publication_date 2005/12/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this Letter, we investigate a class of Hamiltonians which, in addition to the usual center-of-mass momentum conservation, also have center-of-mass position conservation. We find that, regardless of the particle statistics, the energy spectrum is at least q-fold degenerate when the filling factor is p/q, where and are coprime integers. Interestingly, the simplest Hamiltonian respecting this type of symmetry encapsulates two prominent examples of novel states of matter, namely, the fractional quantum Hall liquid and the quantum dimer liquid. We discuss the relevance of this class of Hamiltonian to the search for featureless Mott insulators.