Convergence Problem for Quantum Impurity Systems

How do I use this algorithm? What does that parameter do?
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haaner
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Joined: 26 Jan 2021, 09:06

Convergence Problem for Quantum Impurity Systems

Post by haaner »

Hi!

I am currently trying to calculate the entanglement entropy of a one-dimensional Spin chain with an impurity dot in the middle, i.e., \( J_{xx} = [J,...,J, \lambda J, \lambda J, J, ..., J].\). For testing purposes, I firstly chose \( J_z = 0 \) to compare the results with exact diagonalization methods (non-interacting tight-binding chain via Jordan-Wigner transformation). There appear to be large convergence issues especially for small \( \lambda \) and moderate/large \(N\). I have tried mixing, choosing different initial guesses, and played with the cutoff parameters. If I choose only one impurity bond at the edges, i.e., \( J_{xx} = [\lambda J,..., J]\), everything seems to be okay and I can reproduce results from the literature. My guess is that the initial state should be chosen more wisely than a simple Neel state or related states to account for long range entanglement.

Concretely, I am thinking about getting the ground states for a system with an impurity on the right (left), and combine both ground states to get an initial guess for the impurity in the middle. However, I am not sure how to properly implement the product of two ground states as an initial guess.

Any suggestions/experiences with impurity problems in DMRG would be greatly appreciated!
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Johannes
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Location: TU Munich

Re: Convergence Problem for Quantum Impurity Systems

Post by Johannes »

Sorry for the late reply.
In general, I think DMRG should be suitable for such problems. I could understand that it fails for tiny/zero values of lambda, but for O(1) values of lambda it should definitely work. (In fact, I think that people have successfully used DMRG as an impurity solver for DMFT.)

It might really be an issue of DMRG not being able to re-distribute the charge correctly, although the mixer is supposed to do help for that.
Have you tried starting from a random(ized) state instead of the pure Neel?

Finally, merging two finite/segment states really shouldn't be that hard.
I think I have some function lying around for it, but it's not included in TeNPy yet due to missing documentation and tests.
Remind me about it, if I didn't merge that in a couple of days :roll:

haaner
Posts: 2
Joined: 26 Jan 2021, 09:06

Re: Convergence Problem for Quantum Impurity Systems

Post by haaner »

Hi Johannes,

thank you for your reply (and also sorry for my late reply). I played around with the parameters a bit more, especially with the mixer and the convergence criterion for the entropy, and could now fix my issues. Thanks!

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