Homogeneous binary trees as ground states of quantum critical Hamiltonians

Journal Article · Tue Jun 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.062335· OSTI ID:21439499

Silvi, P ^[1]; Giovannetti, V ^[2]; Montangero, S ^[3]; Rizzi, M; Cirac, J I ^[4]; Fazio, R ^[2]

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1. International School for Advanced Studies (SISSA), Via Bonomea 265, I-34136 Trieste (Italy)
2. NEST, Scuola Normale Superiore and Istituto di Nanoscienze-CNR, I-56127 Pisa (Italy)
3. Institut fuer Quanteninformationsverarbeitung, Universitaet Ulm, D-89069 Ulm (Germany)
4. Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching (Germany)

Many-body states whose wave functions admit a representation in terms of a uniform binary-tree tensor decomposition are shown to obey power-law two-body correlation functions. Any such state can be associated with the ground state of a translationally invariant Hamiltonian which, depending on the dimension of the systems sites, involves at most couplings between third-neighboring sites. Under general conditions it is shown that they describe unfrustrated systems which admit an exponentially large degeneracy of the ground state.

• OSTI ID: 21439499
• Journal Information: Physical Review. A, Vol. 81, Issue 6; Other Information: DOI: 10.1103/PhysRevA.81.062335; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
CORRELATION FUNCTIONS
COUPLING
GROUND STATES
HAMILTONIANS
QUANTUM MECHANICS
TENSORS
TWO-BODY PROBLEM
WAVE FUNCTIONS
ENERGY LEVELS
FUNCTIONS
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MECHANICS
QUANTUM OPERATORS