question about tdvp
Posted: 08 Apr 2019, 09:18
Hi, everyone.
I'm trying to do tdvp, but there are something in the original paper which I cannot understand.
Firstly, why the projector in this form? I know the projector is something like \(1 - \sum_N |\psi_N><\psi_N|\), but what's the target space here, it seems like we project it onto a basis ororthogonal to the original wave-function. I can understand this minus part in two-site tdvp, it's just minus a on-site interaction (since we counter twice on-site interaction in two-site update), is this true?
Secondly, what's the zero-site Hamiltonian? I didn't do the one-site dmrg (I always do the two-site dmrg) before, so I have no knowledge about this. In tenpy, it's just the singular value, but I do not know why we need to minus the singular value. Is this the same in the two-site tdvp? If so, there's a question: in one-site update, we actually only update one singular value in one time. From this reason, I don't know why we need to minus the singular value, or it's different from the two-site tdvp?
Thirdly, if the two-site tdvp is what I said "just minus a on-site interaction", why not simply do lanczos for \(H_{bond}^i - H_{one-site}^{i+1} \otimes Id^i\). In fact, this's what we did before in tebd, it will be much faster than do lanczos twice (one for \(H_{bond}\), another for \(H_{one-site}\)), or I'm wrong with something?
Thanks, Qicheng
I'm trying to do tdvp, but there are something in the original paper which I cannot understand.
Firstly, why the projector in this form? I know the projector is something like \(1 - \sum_N |\psi_N><\psi_N|\), but what's the target space here, it seems like we project it onto a basis ororthogonal to the original wave-function. I can understand this minus part in two-site tdvp, it's just minus a on-site interaction (since we counter twice on-site interaction in two-site update), is this true?
Secondly, what's the zero-site Hamiltonian? I didn't do the one-site dmrg (I always do the two-site dmrg) before, so I have no knowledge about this. In tenpy, it's just the singular value, but I do not know why we need to minus the singular value. Is this the same in the two-site tdvp? If so, there's a question: in one-site update, we actually only update one singular value in one time. From this reason, I don't know why we need to minus the singular value, or it's different from the two-site tdvp?
Thirdly, if the two-site tdvp is what I said "just minus a on-site interaction", why not simply do lanczos for \(H_{bond}^i - H_{one-site}^{i+1} \otimes Id^i\). In fact, this's what we did before in tebd, it will be much faster than do lanczos twice (one for \(H_{bond}\), another for \(H_{one-site}\)), or I'm wrong with something?
Thanks, Qicheng