`max_virtualspaces` throw ArgumentError: Sector has negative dimension

[ZongYongyue]

For large size systems, max_virtualspaces will throw ArgumentError: Sector has negative dimension but it is fine in small size systems.

using TensorKit
using MPSKit
using DynamicalCorrelators: hubbard

#small size system
julia> H = hubbard(Float64, SU2Irrep, U1Irrep, FiniteStrip(2,4);t=1,U=8);
julia> max_virtualspaces(physicalspace(H))
5-element Vector{GradedSpace{ProductSector{Tuple{FermionParity, SU2Irrep, U1Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, SU2Irrep, U1Irrep}}, Int64}}}:
 Vect[(FermionParity ⊠ Irrep[SU₂] ⊠ Irrep[U₁])]((0, 0, 0)=>1)
 Vect[(FermionParity ⊠ Irrep[SU₂] ⊠ Irrep[U₁])]((1, 1/2, 0)=>1, (0, 0, 1)=>1, (0, 0, -1)=>1)
 Vect[(FermionParity ⊠ Irrep[SU₂] ⊠ Irrep[U₁])]((0, 0, 0)=>3, (0, 1, 0)=>1, (1, 1/2, 1)=>2, (1, 1/2, -1)=>2, (0, 0, 2)=>1, (0, 0, -2)=>1)
 Vect[(FermionParity ⊠ Irrep[SU₂] ⊠ Irrep[U₁])]((1, 1/2, 0)=>1, (0, 0, 1)=>1, (0, 0, -1)=>1)
 Vect[(FermionParity ⊠ Irrep[SU₂] ⊠ Irrep[U₁])]((0, 0, 0)=>1)

#lage size system 
julia> H = hubbard(elt, SU2Irrep, U1Irrep, FiniteStrip(8,192);t=1,U=8);
julia> max_virtualspaces(physicalspace(H))
ERROR: ArgumentError: Sector (FermionParity(1) ⊠ Irrep[SU₂](1/2) ⊠ Irrep[U₁](1)) has negative dimension -3252704806379397616
Stacktrace:
 [1] GradedSpace{ProductSector{Tuple{…}}, TensorKit.SortedVectorDict{ProductSector{…}, Int64}}(dims::TensorKit.SortedVectorDict{ProductSector{Tuple{…}}, Int64}; dual::Bool)
   @ TensorKit ~/.julia/packages/TensorKit/hkxhv/src/spaces/gradedspace.jl:55
 [2] GradedSpace
   @ ~/.julia/packages/TensorKit/hkxhv/src/spaces/gradedspace.jl:50 [inlined]
 [3] fuse(V₁::GradedSpace{ProductSector{…}, TensorKit.SortedVectorDict{…}}, V₂::GradedSpace{ProductSector{…}, TensorKit.SortedVectorDict{…}})
   @ TensorKit ~/.julia/packages/TensorKit/hkxhv/src/spaces/gradedspace.jl:167
 [4] max_virtualspaces(Ps::Vector{…}; left::GradedSpace{…}, right::GradedSpace{…})
   @ MPSKit ~/.julia/packages/MPSKit/bM5WR/src/states/finitemps.jl:398
 [5] max_virtualspaces(Ps::Vector{GradedSpace{ProductSector{Tuple{FermionParity, SU2Irrep, U1Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{…}}, Int64}}})
   @ MPSKit ~/.julia/packages/MPSKit/bM5WR/src/states/finitemps.jl:392
 [6] top-level scope
   @ REPL[54]:1

It should have nothing to do with the way the Hamiltonian is defined. I also encounter this error when using hubbard_model in MPSKitModels.

using TensorKit
using MPSKit
using MPSKitModels:hubbard_model
julia> H2 = hubbard_model(Float64, U1Irrep, U1Irrep,FiniteStrip(8, 192);t=1,U=8);
julia> max_virtualspaces(physicalspace(H2))
ERROR: ArgumentError: Sector (FermionParity(0) ⊠ Irrep[U₁](30) ⊠ Irrep[U₁](0)) has negative dimension -7897609303118766016
Stacktrace:
 [1] GradedSpace{ProductSector{Tuple{…}}, TensorKit.SortedVectorDict{ProductSector{…}, Int64}}(dims::TensorKit.SortedVectorDict{ProductSector{Tuple{…}}, Int64}; dual::Bool)
   @ TensorKit ~/.julia/packages/TensorKit/hkxhv/src/spaces/gradedspace.jl:55
 [2] GradedSpace
   @ ~/.julia/packages/TensorKit/hkxhv/src/spaces/gradedspace.jl:50 [inlined]
 [3] fuse(V₁::GradedSpace{ProductSector{…}, TensorKit.SortedVectorDict{…}}, V₂::GradedSpace{ProductSector{…}, TensorKit.SortedVectorDict{…}})
   @ TensorKit ~/.julia/packages/TensorKit/hkxhv/src/spaces/gradedspace.jl:167
 [4] max_virtualspaces(Ps::Vector{…}; left::GradedSpace{…}, right::GradedSpace{…})
   @ MPSKit ~/.julia/packages/MPSKit/bM5WR/src/states/finitemps.jl:398
 [5] max_virtualspaces(Ps::Vector{GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep, U1Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{…}}, Int64}}})
   @ MPSKit ~/.julia/packages/MPSKit/bM5WR/src/states/finitemps.jl:392
 [6] top-level scope
   @ REPL[57]:1

[lkdvos]

That is most definitely an overflow error. Note that the virtual space in the middle of the chain is simply the fusion of the left half of the physical spaces, so in this case you would get a 4^(192/2) dimensional space:

julia> 4^(192÷2)
0

julia> big(4)^(192 ÷ 2)
6277101735386680763835789423207666416102355444464034512896

julia> typemax(Int)
9223372036854775807

max_virtualspaces is really supposed to only be used in cases where you would conceivably construct the full state vector, can you maybe elaborate where this shows up or what you are trying to achieve? Is it really this exponentially large number you would require, or is there different functionality we could provide?

As a sidenote, I'll try and see if it is reasonable to throw a better error and capture this.

[ZongYongyue]

I trid to obtain a rand MPS:

FiniteMPS(rand, elt, physicalspace(H), max_virtualspaces(physicalspace(H); right=right)[2:(end - 1)];right=right)

which follows your test in "Sector conventions":

maxVspaces = MPSKit.max_virtualspaces(physicalspace(H))
gs, = find_groundstate(FiniteMPS(physicalspace(H), maxVspaces[2:(end - 1)]), H;
                           verbosity=0)

[lkdvos]

What I'm doing there is really taking the maximal bond dimension - this is all equivalent to exact diagonalization, mostly for testing purposes. What you really want is to give a reasonable maximal virtual space, otherwise you are asking for the construction of an MPS with an exponential number of parameters in the size, therefore overflowing integers (and exploding memory if you were to actually create the tensors)

[ZongYongyue]

I see, thank you!