2012/10/31 by Carlos Fernández-González, C. Fernández-González, Norbert Schuch +5 · 3 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Degenerate energy levels #Frustration #Gapless playback #Ground state #Hamiltonian (control theory) #Injective function #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Thermodynamic limit #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1007/s00220-014-2173-z
published as Commun. Math. Phys. 333, 299-333 (2015) · 36 pages, new version with some contents rearranged, and a correction in the injective case
openalex publication_date 2014/11/05 · arxiv created 2014/11/24 · arxiv updated 2015/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate ground state (the so-called non-injective case), we construct another 'uncle' Hamiltonian which is local and frustration free but gapless, and its spectrum is \R+. The construction is obtained by linearly perturbing the matrices building up the state in a random direction, and then taking the limit where the perturbation goes to zero. For MPS where the parent Hamiltonian has a unique ground state (the so-called injective case) we also build such uncle Hamiltonian with the same properties in the thermodynamic limit.