apply localMPO to an Itensor

ITensor C++ Questions
1

Hello,

I am trying to apply a localMPO to a local MPS Itensor. Namely

auto PH = LocalMPO(WGlobal);
int b=1;
int numCenter=1
PH.numCenter(numCenter);
PH.position(b,psi);
phi1 = psi(b);
phi1 = PH * phi1;

the latter command cannot compile:

error: invalid operands to binary expression (‘LocalMPO’ and ‘ITensor’)
phi1 = PH * phi1;

What type of object is the local MPO then? How can I extract the corresponden ITensor and apply it to the local MPS?

Thanks a lot!

Jacopo.

2

Could you explain more about what you are trying to do? the LocalMPO object is really designed for a sparse projection of the MPS, where the two main functions are product/expect to find \langle \phi^\prime|PH|\phi\rangle or \langle \phi|PH|\phi\rangle.

Given a standard MPO, one can use the applyMPO function to either exactly, or approximately apply an MPO to a MPS.

3

Hi,

thanks for your answer!
All I am trying to do is to have an Itensor object (with 2 links indeces and sites and site’ ) giving me the 1 site effective Hamiltonian at site b (as in TDVP for example (see Fig 2 in https://arxiv.org/pdf/1408.5056)), and I want to apply it to the MPS at site b. I thought that this Itensor object is indeed given by PH, so that explains my previous attempt to code.

Thanks,
Jacopo.

4

Ah yes, this is the object in Fig 2b (for some number of sites). product is probably the function you want. Check out how things are done in the tdvp code: TDVP/tdvp.h at master · ITensor/TDVP · GitHub

(And an obligatory this is much nicer in the Julia version )

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