search

QuantumKitHub / MPSKit.jl

A Julia package dedicated to simulating quantum many-body systems using Matrix Product States (MPS)
MIT License
126 stars 28 forks source link

IDMRG2 can error when the input state is not full rank #117

Closed lkdvos closed 3 months ago

lkdvos commented 6 months ago

When starting with an InfiniteMPS from tensors that are not full rank, the gauging algorithm does not necessarily lead to square CR tensors. If this happens at the edges of the unitcell, IDMRG2 fails because it takes an inverse of C which is not square.

julia> using MPSKit, TensorKit
julia> As = [MPSTensor(ℂ^2, ℂ^1, ℂ^3), MPSTensor(ℂ^2, ℂ^3, ℂ^4), MPSTensor(ℂ^2, ℂ^4, ℂ^1)];

julia> psi = InfiniteMPS(As)
3-site InfiniteMPS:
│   ⋮
│ CR[3]: TensorMap(ℂ^1 ← ℂ^1)
├── AL[3]: TensorMap((ℂ^4 ⊗ ℂ^2) ← ℂ^1)
├── AL[2]: TensorMap((ℂ^2 ⊗ ℂ^2) ← ℂ^4)
├── AL[1]: TensorMap((ℂ^1 ⊗ ℂ^2) ← ℂ^2)
│   ⋮

julia> space.(psi.CR)
3-element PeriodicArray{TensorMapSpace{ComplexSpace, 1, 1}, 1}:
 ℂ^2 ← ℂ^2
 ℂ^4 ← ℂ^2
 ℂ^1 ← ℂ^1

In general, there are many subtle problems for MPS tensors that aren't full rank, so I think we should both add an explicit check in the InfiniteMPS constructor that prohibits this, as well as provide a mechanism for creating full rank MPS tensors from non-full rank ones.

partial stack trace for completeness:

LoadError: SpaceMismatch("codomain ProductSpace(Vect[(FermionParity ⊠ Irrep[U₁] ⊠ Irrep[SU₂])]((0, 0, 0)=>16, (0, 4, 0)=>35, (0, -4, 0)=>1, (0, 8, 0)=>16, (0, 12, 0)=>1, (1, 2, 1/2)=>44, (1, -2, 1/2)=>8, (1, 6, 1/2)=>44, (1, 10, 1/2)=>8, (0, 0, 1)=>22, (0, 4, 1)=>51, (0, -4, 1)=>1, (0, 8, 1)=>22, (0, 12, 1)=>1, (1, 2, 3/2)=>28, (1, -2, 3/2)=>4, (1, 6, 3/2)=>28, (1, 10, 3/2)=>4, (0, 0, 2)=>6, (0, 4, 2)=>17, (0, 8, 2)=>6, (1, 2, 5/2)=>4, (1, 6, 5/2)=>4, (0, 4, 3)=>1)) and domain ProductSpace(Vect[(FermionParity ⊠ Irrep[U₁] ⊠ Irrep[SU₂])]((0, 0, 0)=>3, (0, 4, 0)=>1, (0, -4, 0)=>1, (1, 2, 1/2)=>2, (1, -2, 1/2)=>2, (0, 0, 1)=>1)) are not isomorphic: no inverse")
Stacktrace:
 [1] inv(t::TensorMap{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, 1, 1, ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Matrix{ComplexF64}}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 1, 0, 0, Nothing}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 1, 0, 0, Nothing}})
   @ TensorKit ~/.julia/packages/TensorKit/gpuAY/src/tensors/linalg.jl:268
 [2] find_groundstate(ost::InfiniteMPS{TensorMap{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, 2, 1, ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Matrix{ComplexF64}}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 2, 0, 1, Nothing}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 1, 0, 0, Nothing}}, TensorMap{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, 1, 1, ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Matrix{ComplexF64}}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 1, 0, 0, Nothing}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 1, 0, 0, Nothing}}}, H::MPOHamiltonian{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, TensorMap{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, 2, 2, ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Matrix{ComplexF64}}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 2, 0, 1, Nothing}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 2, 0, 1, Nothing}}, ComplexF64}, alg::IDMRG2{KrylovKit.Arnoldi{KrylovKit.ModifiedGramSchmidt2, Float64}}, oenvs::MPSKit.MPOHamInfEnv{MPOHamiltonian{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, TensorMap{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, 2, 2, ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Matrix{ComplexF64}}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 2, 0, 1, Nothing}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 2, 0, 1, Nothing}}, ComplexF64}, TensorMap{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, 2, 1, ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Matrix{ComplexF64}}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 2, 0, 1, Nothing}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 1, 0, 0, Nothing}}, InfiniteMPS{TensorMap{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, 2, 1, ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Matrix{ComplexF64}}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 2, 0, 1, Nothing}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 1, 0, 0, Nothing}}, TensorMap{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, 1, 1, ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Matrix{ComplexF64}}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 1, 0, 0, Nothing}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 1, 0, 0, Nothing}}}, KrylovKit.GMRES{KrylovKit.ModifiedGramSchmidt2, Float64}})
   @ MPSKit ~/.julia/packages/MPSKit/JT8u6/src/algorithms/groundstate/idmrg.jl:116
 [3] find_groundstate(ost::InfiniteMPS{TensorMap{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, 2, 1, ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Matrix{ComplexF64}}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 2, 0, 1, Nothing}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 1, 0, 0, Nothing}}, TensorMap{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, 1, 1, ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Matrix{ComplexF64}}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 1, 0, 0, Nothing}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 1, 0, 0, Nothing}}}, H::MPOHamiltonian{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, TensorMap{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Int64}}, 2, 2, ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, Matrix{ComplexF64}}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 2, 0, 1, Nothing}, FusionTree{ProductSector{Tuple{FermionParity, U1Irrep, SU2Irrep}}, 2, 0, 1, Nothing}}, ComplexF64}, alg::IDMRG2{KrylovKit.Arnoldi{KrylovKit.ModifiedGramSchmidt2, Float64}})
   @ MPSKit ~/.julia/packages/MPSKit/JT8u6/src/algorithms/groundstate/idmrg.jl:85