Add correlator for InfinitePEPO (mixed state) #274
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lkdvos
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lkdvos
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Overall looks good to me!
I do think I slightly disgree with putting the logic for the correlators in the contractions folder. If possible, I think I would put only the contractions there, while keeping the actual correlator logic in a separate file.
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I can move the redefinition |
lkdvos
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lkdvos
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I think my original motivation for the contractions folder was to have a place to put an implementation for some of the contractions that clutter up the main logic of the algorithms. So in some sense, I would have put only the @tensor calls in there, and the generated functions.
I do think the algorithms/correlators.jl file made sense, so I would rather keep that logic there if you don't mind.
I additionally had a look in a bit more detail about the transfer logic, and I think it would make more sense to follow the previous/other strategies a bit closer, rather than using _transfer_left directly.
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Your PR no longer requires formatting changes. Thank you for your contribution! |
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I have moved correlator_horizontal, correlator_vertical and the extension of MPSKit.correlator back to src/algorithms/correlators.jl.
To really using the V * T syntax, I need some help in figuring out the fermion twists to be added to the planar transfer_left.
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Okay, to move forward with this. While it does kind of stall progress here, I think it's not too much of a detour to properly address the transfer function confusion between MPS and CTMRG environments here. I would suggest to
I can give this a go tomorrow morning. Having originally introduced the As a side note, having to think about all of this again made me realize that probably our correlation length implementation is most likely just wrong for fermionic systems. We currently compute a transfer matrix spectrum using (in the end) |
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I suggest the slightly more verbose names |
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I don't think this is linked to CTM though, I would argue that actually there might even be a case to be made for just using |
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I had a go at the edge transfer matrices like I said. I think I changed all the relevant bits, and also updated the correlation length implementation in the process so that should now work for symmetries with non-trivial twists. Some things I'm not entirely sure about:
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There are problems when the physical space is a dual space. I'll try to solve them later. |
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@lkdvos I'm now sure that either using Random
using TensorKit
using PEPSKit
Random.seed!(0)
V1 = Vect[FermionParity](0 => 2, 1 => 2)
V = V1' ⊗ V1' ⊗ V1
# create a positive operator
ρ = randn(V → V)
ρ = ρ * ρ'
A = id(V)
PEPSKit.trmul(A, ρ) / PEPSKit.str(ρ) # not equal to 1 |
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Yeah, these functions don't actually do anything particularly smart, I think they really just build the |
leburgel
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leburgel
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I added some commentary on things that I think should be reviewed again, other than those this seems good to go for me.
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This PR generalizes
correlatorto calculate correlation functions ⟨O(i, j)⟩ between two sites (i, j) in the same row/column in a 1-layer InfinitePEPO ρ (mixed state). Only tr(ρO) is implemented. ⟨ρ|O|ρ⟩ is not intended to be treated here.To do: