Matrix product state and mean-field solutions for one-dimensional systems can be found efficiently

Journal Article · Thu Jul 15 04:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.012314· OSTI ID:21440482

Schuch, Norbert ^[1]; Cirac, J Ignacio ^[1]

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1. Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching (Germany)

We consider the problem of approximating ground states of one-dimensional quantum systems within the two most common variational ansatzes, namely, the mean-field ansatz and matrix product states. We show that both for mean field and for matrix product states of fixed bond dimension, the optimal solutions can be found in a way which is provably efficient (i.e., scales polynomially). This implies that the corresponding variational methods can be in principle recast in a way which scales provably polynomially. Moreover, our findings imply that ground states of one-dimensional commuting Hamiltonians can be found efficiently.

• OSTI ID: 21440482
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 82; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CALCULATION METHODS
COMMUTATION RELATIONS
ENERGY LEVELS
GROUND STATES
HAMILTONIANS
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
MATRICES
MEAN-FIELD THEORY
ONE-DIMENSIONAL CALCULATIONS
QUANTUM OPERATORS
QUANTUM STATES
VARIATIONAL METHODS