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Arbitrary initial state and exact "toExpH"?

+1 vote
asked by (1.2k points)

Hi Miles,

I have two quick questions.

  1. Is there a way to convert an arbitrary vector to MPS or IQMPS as an initial state?

  2. I wanted to exponentiate the Hamiltonian exactly for time evolution of small systems. But toExpH(ampo, tau) is only approximately equal to exp(-tau*H) up to terms of order tau^2. How can I do it exactly?

Thanks for all your help.

Jin

1 Answer

+1 vote
answered by (70.1k points)

Hi, so I don't fully understand your question #1. Do you mean an abitrary vector in the full Hilbert space? If so, yes one could do this but there's no such function defined in ITensor currently. You would have to write it (basically it would be a sequence of SVDs).

About #2, there's no way I know of to exponentiate MPO's exactly in general. For the special case of a Hamiltonian where all the terms commute it can be done, though. (See the paper by Pirvu, Murg, Cirac, and Verstraete from 2010 for details.)

commented by (1.2k points)
Hi, for Question #1, that's what I mean. Thanks a lot.
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