non-local correlations for a chain

[fegarciaga]

Hello,

I was wondering if there is a way to measure non-local correlations in a chain architecture when doing PT-TEMPO. Would I need to use expectations? In particular I'm interested in computing a three body operator defined on three consecutive sites of my chain architecture. Thank you for the help

[piperfw]

Hi @fegarciaga, as you probably found out the TEBD method in OQuPy currently supports nearest neighbour interactions only, so I don't believe you can immediately tackle the three body operator problem.

Whether the method can be extended beyond nearest neighbour is an interested question, I expect in principle yes - provided a MPS remains a good representation of the state - but would be quite a task to implement in code.

[piperfw]

Hi again @fegarciaga, I misread your question as asking for multisite terms in the Hamiltonian - apologies!

Multisite correlations are possible in OQuPy, and yes you do essentially need to make use of a expectations method. The trick is that with PT-TEBD, you need to specify which combination of site dynamics you want ahead of time.

For example, suppose I have a chain of 5 sites and want to get the dynamics for sites 1 and 2 individually, and 1,2,3 together. Then I would set

dynamics_sites=[1,2,(1,2,3)]

where the tuple indicates you want multisite rather than individual site dynamics.

A PT-TEBD object is created with something like

pt_tebd = oqupy.PtTebd(
    initial_augmented_mps=initial_augmented_mps,
    system_chain=system_chain,
    process_tensors=[pt, pt, pt, pt, pt],
    parameters=pt_tebd_params,
    dynamics_sites=dynamics_sites,
    chain_control=None)

and then dynamics computed using

results = pt_tebd.compute(num_steps)

more details can be found in the 'Chains and PT-TEBD' tutorial notebook.

One can get the required dynamics from the returned results as follows:

site1_dynamics = results['dynamics'][1]
site2_dynamics = results['dynamics'][2]
sites123_dynamics = results['dynamics'][(1,2,3)]

These are standard 'Dynamics' objects in OQuPy which means you can both get a list of states for each timestep, e.g. sites123_dynamics.states, from which a trace with an 3 body operator (matrix) gives an expectation, or get the list of corresponding expectations directly from sites123_dynamics.expectations(OP) where OP is your three body operator on the Hilbert space of the three sites (e.g. for spins this would be an 8x8 matrix).

Hope that helps!

[fegarciaga]

Thank you so much!

[piperfw]

No problem, I'll mark the issue as solved but if you need any further help or have other questions just add a comment here and I should be able to pick up on it (I'm away for a week or so from this Friday however).

Edit: I'll leave it open for now in case closing it prevents you from commenting... can't remember how that works exactly.