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As far as I understand one can only use MERA(Multiscale Entanglement Renormalization Ansatz) to find ground state for Hamiltonians of following form(with possible simplifications due to additional symmetries):

$$H =\sum_{i} h^{[i,i+1]}$$

I can see from the article of Vidal that the whole algorithm is based on aforementioned form of Hamiltonian.
My question is whether one can still use MERA for more complicated(non-local) Hamiltonians? Or is there any principal problem which prevents us from doing that?
Suppose it is impossible. Are there any generalisations of MERA(or may be other kinds of tensor networks) which deal with non-local Hamiltonians?

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  • $\begingroup$ How non-local should the Hamiltonian be? Two-body but long-ranged? Many-body, but tensor product? More general? And does "can be applied" to the suitability of the ansatz, to the cost of the numerical procedure, or its convergence? $\endgroup$ – Norbert Schuch Nov 25 '16 at 15:35

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