Nonlinear minimisation

[nikitn2]

Hello,

First of all, thank you so much for creating and maintaining this fantastic tensor networks library – I really love how flexible and well-written it is!

My question is simple. Let H = H( |psi> ) be some nonlinear Hamiltonian that depends (perhaps linearly, or quadratically) on a |psi> matrix product state. How do I best minimise <psi| H | psi> with Quimb?

Should I edit the in-built DMRG or imaginary time-evolution routines, or is it better if I just wrote my own DMRG script from scratch where the local (nonlinear) updates are solved using an autodifferentiation scheme? Any advice and/or ideas would be much welcome :)

Cheers!

[nikitn2]

Bump :)

[jcmgray]

Hi @nikitn2, sorry it's a bit of tricky question to answer. The question is minimizing
$$\langle \psi | H(\psi) | \psi \rangle$$
right? Without knowing much about the structure of $H(\psi)$ I would have thought autodiff is the best way to go. With a DMRG style approach the environments would be pre-computed and therefore solving the local system is not going to account for the effect of $\psi$ on the environment no? Unless the changes are very small - in which case you are likely doing a very inefficient sort of gradient descent.

[nikitn2]

OK, thanks a lot, makes sense :) I'll try to play around with some different ideas I have, and eventually report back here!