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OpStrings

TenNetLib.jl provides an alternative, called OpStrings, to ITensors.jl's OpSum to automatically construct Hamiltonains / operators. TenNetLib.jl's own CouplingModel is built from OpStrings and is not compatible with OpSum.

OpString

OpStrings is basically a vector of OpString objects (notice the difference in 's' at the end)

TenNetLib.OpString — Type
struct OpString{T <: Number}
    coeff::T
    ops::Vector{Pair{String, Int}}
end

Holds operator strings (operator names with corresponding positions) along with the coefficient.

  • coeff::T: Coeffcient of the operator string.
  • ops::Vector{Pair{String, Int}}: String of operator names along with the positions.
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TenNetLib.minsite — Method
function minsite(opstr::OpString)

Returns the lowest site position in the operator string of the OpString.

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TenNetLib.maxsite — Method
function maxsite(opstr::OpString)

Returns the highest site position in the operator string of the OpString.

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TenNetLib.removeIds — Method
function removeIds(opstr::OpString{T}) where {T <: Number}

Returns an OpString with all "Id" operators removed from the original.

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TenNetLib.bosonize — Method
function bosonize(opstr::OpString{T1},
                  sites::Vector{Index{T2}}) where {T1 <: Number, T2}

Returns an OpString after "bosonizing" the original with Jordan-Wigner strings as needed. See bosonize.

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OpStrings

TenNetLib.OpStrings — Type
const OpStrings{T} = Vector{OpString{T}}

Collection of OpStrings.

Syntax:

os = OpStrings()
os += 1, "Sx" => i, "Sx" => j, "Sx" => k, ....
os += "Sx" => i, "Sx" => j, "Sx" => k, ....

Example:

os = OpStrings()    
for j=1:N-1
    os += 1, "Sz" => j, "Sz" => j+1
    os += 0.5, "S+" => j, "S-" => j+1
    os += 0.5, "S-" => j, "S+" => j+1
end
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TenNetLib.removeIdsZeros — Method
function removeIdsZeros(os::OpStrings{T}) where {T <: Number}

Returns an OpStrings with all "Id" operators removed from the original, as well as any OpString term that has coeff less than Float64_threshold().

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TenNetLib.bosonize — Method
function bosonize(os::OpStrings{T1}, sites::Vector{Index{T2}}) where {T1 <: Number, T2}

Returns an OpStrings after "bosonizing" the original with Jordan-Wigner strings as needed. See bosonize.

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TenNetLib.mergeterms — Method
function mergeterms(os::OpStrings{T}) where T <: Number

Returns an OpStrings where OpString elements with exactly same operator strings has been merged by adding the coefficients.

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MPO from OpStrings

ITensors.MPO — Method
function ITensors.MPO(os::OpStrings{T1},
                      sites::Vector{Index{T2}};
                      maxdim::Int = typemax(Int),
                      mindim::Int = 1,
                      cutoff::Float64 = Float64_threashold(),
                      svd_alg::String = "divide_and_conquer",
                      chunksize::Int = 12) where {T1 <: Number, T2}

Creates MPO from os::OpStrings. The present version uses recursive SVDs to create the MPO. Very inefficient when number of Hamiltonian terms is large. Future updates will solve the problem.

Named arguments and their default values:

  • maxdim::Int = typemax(Int): Maximum MPO bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum MPO bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".
  • chunksize::Int = 12. Maximum size of the chunks on which recursive SVDs are performed.
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