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
Real-time evolution of the GS of the U=0 Fermi-Hubbard model
Re: Real-time evolution of the GS of the U=0 Fermi-Hubbard model
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
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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Re: Real-time evolution of the GS of the U=0 Fermi-Hubbard model
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
Re: Real-time evolution of the GS of the U=0 Fermi-Hubbard model
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 ![Wink ;-)](./images/smilies/icon_e_wink.gif)
![Smile :)](./images/smilies/icon_e_smile.gif)
![Wink ;-)](./images/smilies/icon_e_wink.gif)
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- Joined: 08 Jan 2019, 03:03
Re: Real-time evolution of the GS of the U=0 Fermi-Hubbard model
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.
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- Joined: 08 Jan 2019, 03:03
Re: Real-time evolution of the GS of the U=0 Fermi-Hubbard model
I notice that this is still not been done, perhaps I can help to write this part.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
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