I'm trying to implement the infinite TDVP algorithm based on these notes

https://arxiv.org/abs/1810.07006

It seems like these are the main steps:

1) Find the left and right environments

2) Use these to create effective Hamiltonians 0, and 1 site.

3) Integrate the TDVP equations to update the MPS tensors.

My question is, once I have update the MPS tensors, should I create a new left and right environment from these for further time evolution? Or can I just multiply this into the environments to update them? My intuition says I need to recreate the environment, but this seems quite expensive to have to do this for every time step, so I was wondering if there's a quicker way.

## Question about iTDVP

### Re: Question about iTDVP

Yes, I think you need to recreate the environments from scratch.

Not completely sure, but I think you could try using the old ones as an initial guess for the new environments.

Not completely sure, but I think you could try using the old ones as an initial guess for the new environments.