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Variational numerical renormalization group methods in one and higher dimensions
Probability| Speaker: | Frank Verstrae, Caltech |
| Location: | 693 Kerr |
| Start time: | Tue, Nov 29 2005, 3:10PM |
Description
The numerical renormalization group methods of K. Wilson and S. White
can be reformulated as variational one-dimensional methods on the set of
so-called finitely correlated or matrix product states. In this talk we
will show how these methods can be generalized to higher dimensions and
how dynamical properties can be calculated. Within this formalism, we
will prove the extraordinary accuracy of the numerical renormalization
methods in the case of one-dimensional systems by using tools from the
field of quantum information theory. We will also discuss the
properties of the higher dimensional generalizations of matrix product
states such as exemplified by the cluster states (a universal resource
for quantum computation), the toric code states of A. Kitaev (exhibiting
topological quantum order) and the resonating valence bond states.