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Real-time evolution of the GS of the U=0 Fermi-Hubbard model

How do I use this algorithm? What does that parameter do?
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jkbs
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Joined: 08 Nov 2019, 15:35

Real-time evolution of the GS of the U=0 Fermi-Hubbard model

Post by jkbs »

Dear Johannes,

I am running some real-time evolution simulations in TeNpy.

First, I simply find the GS of the U=0 Fermi-Hubbard model using infinite DMRG. This is a gapless state, so I cannot fully get a converged result, but I get convergence to three digits in the energy if I use chi=200.

Then, I take this state (chi=200) and evolve it under the influence of the U=0 Fermi-Hubbard model using infinite TEBD. I am doing this as a test for other things. Here, since I am evolving an eigenstate of the Hamiltonian, I should not get any change of the state. I indeed get an energy that remains constant with time.
The entanglement entropy and the bond dimension grow very fast (chi grows to 2000 before time 1.0 with a discarded weight of 10^-6).

I can justify this to myself as I understand that the initial state I am evolving is not actually fully represented by a finite bond dimension MPS, so that might be acceptable.

But, is it really? I'd expect this to happen over a much longer timescale. I wanted to ask you if you believe this is okay or whether there might be some issues with the TEBD code.

Thank you so much and best regards,
KBS

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Johannes
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Joined: 21 Jul 2018, 12:52
Location: UC Berkeley

Re: Real-time evolution of the GS of the U=0 Fermi-Hubbard model

Post by Johannes »

What order (second or fourth) and timestep do you use for TEBD?
Does this go away if you simply use a smaller timestep/higher order?
Did you try to look at the overlap with the initial ground state returned by DMRG (as a function of time)?

Converging just 3 digits in energy still a bit unprecise, maybe the ground state is still quite bad.
I'm currently working on a function to evaluate the variance of H, which can serve as a check for the quality of the ground state.

By the way, which version of TeNPy are you using? The infinite DMRG was rewritten a bit by Leon, the current version is 0.4.1.

Best,
Johannes

QichengTang
Posts: 32
Joined: 08 Jan 2019, 03:03

Re: Real-time evolution of the GS of the U=0 Fermi-Hubbard model

Post by QichengTang »

it is a good idea to write a function to evaluate the variance of H, and maybe something like |<\psi|H|\psi>|^2 - <\psi|H^2|\psi> can be used in dmrg to be a control parameter?
Johannes wrote:
11 Nov 2019, 15:50
What order (second or fourth) and timestep do you use for TEBD?
Does this go away if you simply use a smaller timestep/higher order?
Did you try to look at the overlap with the initial ground state returned by DMRG (as a function of time)?

Converging just 3 digits in energy still a bit unprecise, maybe the ground state is still quite bad.
I'm currently working on a function to evaluate the variance of H, which can serve as a check for the quality of the ground state.

By the way, which version of TeNPy are you using? The infinite DMRG was rewritten a bit by Leon, the current version is 0.4.1.

Best,
Johannes

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Johannes
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Posts: 176
Joined: 21 Jul 2018, 12:52
Location: UC Berkeley

Re: Real-time evolution of the GS of the U=0 Fermi-Hubbard model

Post by Johannes »

Yes, that's for sure a good idea. Indeed, I thought about it and started to implement it already a few days ago, but I'm quite busy these days (moving to UC Berkeley :)), so I didn't have time to finish it. Hopefully, I can find a bit time next week - unless you volunteer to time to implement it ;-)

QichengTang
Posts: 32
Joined: 08 Jan 2019, 03:03

Re: Real-time evolution of the GS of the U=0 Fermi-Hubbard model

Post by QichengTang »

Sorry for the late reply, I just see your message.
Last edited by QichengTang on 11 Mar 2020, 04:58, edited 2 times in total.

QichengTang
Posts: 32
Joined: 08 Jan 2019, 03:03

Re: Real-time evolution of the GS of the U=0 Fermi-Hubbard model

Post by QichengTang »

Johannes wrote:
14 Nov 2019, 10:13
Yes, that's for sure a good idea. Indeed, I thought about it and started to implement it already a few days ago, but I'm quite busy these days (moving to UC Berkeley :)), so I didn't have time to finish it. Hopefully, I can find a bit time next week - unless you volunteer to time to implement it ;-)
I notice that this is still not been done, perhaps I can help to write this part.

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