Implement cluster expansion MPOs #252
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Perhaps also using |
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Keep in mind that @generated tends to increase compilation time, since it has to compile new functions for all types.
Having a quick glance at this, it seems to me that the compile time is this large mostly because a lot of the functions are very type-unstable. One thing that might help is to use Val(N) whenever you are referring to the lengths of the finite mpos. Since you are instantiating them as contracted tensors, this yields AbstractTensorMap{T,S,N,N} or similar objects, and becomes a problem when N is not known at compile time.
(which coincidentally also requires more @generated functions since ncon is also not type stable 😁 )
This being said, am I right in looking at this and thinking the main missing components in terms of contractions is the instantiation or application of FiniteMPO with static lengths?
If this is the case, we might just create SFiniteMPO in analogy to SVector (StaticArrays.jl), and implement this generically? This has additional benefits as well, since the derivatives would fit in this same framework.
| :(return @tensor $t_out := $t_left * $t_right)) | ||
| end | ||
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| function _make_apply_functions(O::SparseBlockTensorMap, n::Int) |
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I'm not entirely sure returning an anonymous function is a great idea here. If you could refactor this into a callable struct, or any struct that you make work with KrylovKit.jl would avoid that you have to recompile these functions every time you call this.
| nT = (n - 1) ÷ 2 | ||
| Al, Ar = make_envs(O, n) | ||
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| fun = if iseven(n) |
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Splitting on the value of n is again very type-unstable...
| lmax = N ÷ 2 # largest level | ||
| τ = -im * dt | ||
| # spaces | ||
| P = physicalspace(H)[1] |
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| P = physicalspace(H)[1] | |
| P = physicalspace(H, 1) |
| τ = -im * dt | ||
| # spaces | ||
| P = physicalspace(H)[1] | ||
| D = dim(physicalspace(H)[1]) # physical dimension |
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| D = dim(physicalspace(H)[1]) # physical dimension | |
| D = dim(P) # physical dimension |
| # spaces | ||
| P = physicalspace(H)[1] | ||
| D = dim(physicalspace(H)[1]) # physical dimension | ||
| V = BlockTensorKit.oplus([ℂ^(D^2l) for l in 0:lmax]...) |
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This seems odly specific to non-symmetric tensors. Not having looked at the paper, is it just oplus([fuse(P^(2l)) for l in 0:lmax])?
| V = BlockTensorKit.oplus([ℂ^(D^2l) for l in 0:lmax]...) | ||
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| TT = tensormaptype(ComplexSpace, 2, 2, ComplexF64) | ||
| O = SparseBlockTensorMap{TT}(undef, V ⊗ P ← P ⊗ V) |
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Can this be written with similar?
| # assign the new level to O | ||
| O[jnl, 1, 1, jnl] = Onew | ||
| elseif iseven(n) # linear problem + svd | ||
| U, S, V = tsvd(Onew, (1, 2, 4), (3, 5, 6)) |
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| U, S, V = tsvd(Onew, (1, 2, 4), (3, 5, 6)) | |
| U, S, V = tsvd!(Onew, (1, 2, 4), (3, 5, 6)) |
| elseif iseven(n) # linear problem + svd | ||
| U, S, V = tsvd(Onew, (1, 2, 4), (3, 5, 6)) | ||
| # assign the new levels to O | ||
| O[jnl - 1, 1, 1, jnl] = permute(U * sqrt(S), ((1, 2), (3, 4))) |
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| O[jnl - 1, 1, 1, jnl] = permute(U * sqrt(S), ((1, 2), (3, 4))) | |
| @plansor O[jnl - 1, 1, 1, jnl][-1 -2; -3 -4] := U[-1 -2 -3; 1] * sqrt(S)[1, -4] |
Writing this with @plansor calls makes it compatible with fermions, and can help with allocations in the future.
| function _fully_contract_O(O::SparseBlockTensorMap, n::Int) | ||
| # Make projector onto the 0 subspace of the virtual level | ||
| Pl = zeros(ComplexF64, ℂ^1 ← space(O, 1)) | ||
| Pl[1] = 1 |
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This pattern seems wrong (and probably will break once I actually get to fixing that), and probably only works for non-symmetric tensors... If I get this right, you want a trivial unit tensor as the first element, so you should probably just instantiate that tensor. There are some examples of this scattered throughout MPSKit 😉
| return be - bo | ||
| end | ||
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| function _fully_contract_O(O::SparseBlockTensorMap, n::Int) |
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Why is this function different from the _make_Hamterms implementation? it seems to me like the exact same contraction as convert(TensorMap, mpo) unless I'm missing something?
This is my initial implementation for the "Symmetric cluster expansions" introduced in https://doi.org/10.1103/PhysRevA.103.L020402
They are currently only implemented for infinite systems.
The current implementation is still undergoing testing and suffers from a rather large compilation time.
Things that still need to be done: