2006/10/20 by Lukasz Fidkowski, Michael Freedman, Fidkowski, Lukasz +7 · 5 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #FOS: Physical sciences #Hamiltonian (control theory) #Hilbert space #Lattice (music) #Mathematical Physics (math-ph) #Mathematical physics #Mathematics #Physics #Quantum chaos and dynamical systems #Quantum many-body systems #Quantum mechanics #Spins #Statistical Mechanics (cond-mat.stat-mech) #String (physics) #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics #Theoretical physics #Wave function #cond-mat.stat-mech #cond-mat.str-el #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.cond-mat/0610583
published in arXiv (Cornell University) (Cornell University) · 13 pages
arxiv created 2006/10/20 · openalex publication_date 2006/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We discuss Hilbert spaces spanned by the set of string nets, i.e. trivalent graphs, on a lattice. We suggest some routes by which such a Hilbert space could be the low-energy subspace of a model of quantum spins on a lattice with short-ranged interactions. We then explain conditions which a Hamiltonian acting on this string net Hilbert space must satisfy in order for its ground state and low-lying quasiparticle excitations to be in the DFib topological phase. Using the string net wavefunction, we describe the properties of this phase. Our discussion is informed by mappings of string net wavefunctions to the chromatic polynomial and the Potts model.