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

How do I use this algorithm? What does that parameter do?
jkbs
Posts: 1
Joined: 08 Nov 2019, 15:35

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

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

Johannes
Posts: 127
Joined: 21 Jul 2018, 12:52
Location: UC Berkeley

### 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

QichengTang
Posts: 26
Joined: 08 Jan 2019, 03:03

### 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

Johannes
Posts: 127
Joined: 21 Jul 2018, 12:52
Location: UC Berkeley

### 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

QichengTang
Posts: 26
Joined: 08 Jan 2019, 03:03