Suggestions for computing entanglement eigenvectors

How do I use this algorithm? What does that parameter do?
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entevecs
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Joined: 15 Apr 2019, 16:46

Suggestions for computing entanglement eigenvectors

Post by entevecs »

Maybe I'm missing something, but in addition to computing the entanglement spectrum, I'm curious to look at some of the low-lying entanglement eigenvectors -- is this prohibitively expensive because it involves explicitly constructing the reduced density matrix?
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Johannes
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Re: Suggestions for computing entanglement eigenvectors

Post by Johannes »

What exactly do you mean by computing the entanglement eigenvectors?
The eigenvectors of which matrix?
For a finite system, I could imagine to look at individual Schmidt vectors (=singular vectors) on the left or right of a given cut in the form of an MPS. You can obtain them by just the part of the MPS left to a given cut, and projecting the open virtual bond at the cut into the index of the index of the Schmidt vector you want to look at. If you want to, you can easily write a function returning them.

For an infinite system, it would correspond to an half-infinite MPS, which is harder to write down...
entevecs
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Joined: 15 Apr 2019, 16:46

Re: Suggestions for computing entanglement eigenvectors

Post by entevecs »

What I had in mind were the eigenvectors diagonalizing \(\mathcal{H}_A\) where \(\rho_A \propto e^{-\mathcal{H}_A}\) (suppose \(A\) is a sub-region of a finite system).

I suppose these are probably related to the Schmidt vectors that you've mentioned. Would one access these for an MPS via: tenpy.networks.mpo.MPS.canonical_form_finite()?
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