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Approximation of Functionals of Hermitian Matrices represented as MPOs

Moritz August, Institut für Informatik, TU München

25.01.2017 at 14:00 

I will present a method to approximate functionals $\mathrm{Tr} f(A)$, such as the entropy, trace norm and to some extent expectation values, of Matrix Product Operators, which is based on the reformulation of a block Lanczos algorithm in tensor network format. I will state the main properties of the method and show how we adapted the basic block  Lanczos algorithm to the tensor network formalism. Following that, I ill give a brief analysis of the complexity and effective runtime of the method and conclude with some numerical evidence that it yields good approximations of the entropy at the example of Gibbs states.

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