Matrix Product State and mean field solutions for one-dimensional systems can be found efficiently

Details Matrix Product State and mean field solutions for one-dimensional systems can be found efficiently Matrix Product State and mean field solutions for one-dimensional systems can be found efficiently

2009-10-22

arxiv.org/abs/0910.4264v2

Phys. Rev. A 82, 012314 (2010)

Physics

Quantum Physics

5 pages; v2: accepted version, Journal-ref added

Scientific paper

10.1103/PhysRevA.82.012314

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.

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