Real-time evolution of the GS of the U=0 Fermi-Hubbard model
Posted: 08 Nov 2019, 15:40
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
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