Hamiltonian construction (untested)
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ysyapa
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@ -9,6 +9,9 @@ struct Hamiltonian{T}
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K_partial::Matrix{Complex{T}}
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K_diag::Union{CuTensor{Complex{T}},Nothing}
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K_mixed::Union{CuTensor{Complex{T}},Nothing}
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K_partial_1x::Union{Matrix{Complex{T}},Nothing}
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K_partial_1y::Union{Matrix{Complex{T}},Nothing}
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K_partial_1z::Union{Matrix{Complex{T}},Nothing}
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Vs::Union{Array{Complex{T}},CuArray{Complex{T}}}
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hermitian::Bool
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mode::Hamiltonian_backend
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@ -16,25 +19,27 @@ struct Hamiltonian{T}
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function Hamiltonian{T}(s::system{T}, V_twobody::Function, ϕ::Real, n_image::Int, mode::Hamiltonian_backend) where {T<:Float}
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@assert mode != gpu_cutensor || CUDA.functional() && CUDA.has_cuda() && CUDA.has_cuda_gpu() "CUDA not available"
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k = -s.N÷2:s.N÷2-1
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Vs = calculate_Vs(s, V_twobody, convert(T, ϕ), n_image)
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hermitian = ϕ == 0.0
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K_partial = (exp(-im * convert(T, ϕ)) * im / sqrt(2 * s.μ)) .* ∂_1DOF.(Ref(s), k, k')
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K_diag = nothing
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K_mixed = nothing
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K_partial_1x, K_partial_1y, K_partial_1z = sym_reduce(s, K_partial)
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Vs = calculate_Vs(s, V_twobody, convert(T, ϕ), n_image)
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if mode == gpu_cutensor
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K_diag = CuTensor(CuArray(K_partial * K_partial), ['a', 'A'])
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K_mixed = CuTensor(CuArray(K_partial), ['a', 'A']) * CuTensor(CuArray(K_partial), ['b', 'B'])
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Vs = CuArray(Vs)
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else
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K_diag = nothing
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K_mixed = nothing
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end
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return new{T}(s, K_partial, K_diag, K_mixed, Vs, hermitian, mode)
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return new{T}(s, K_partial, K_diag, K_mixed, K_partial_1x, K_partial_1y, K_partial_1z, Vs, hermitian, mode)
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end
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end
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Base.size(H::Hamiltonian, i::Int)::Int = (i == 1 || i == 2) ? H.s.N^(H.s.d * (H.s.n - 1)) : throw(ArgumentError("Hamiltonian only has 2 dimesions"))
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Base.size(H::Hamiltonian, i::Int)::Int = (i == 1 || i == 2) ? H.s.N^(H.s.d * (H.s.n - 2)) * H.dim1 : throw(ArgumentError("Hamiltonian only has 2 dimesions"))
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Base.size(H::Hamiltonian)::Dims{2} = (size(H, 1), size(H, 2))
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"Dimensions of a vector to which 'H' can be applied"
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vectorDims(H::Hamiltonian)::Dims = tuple(fill(H.s.N, H.s.d * (H.s.n - 1))...)
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vectorDims(H::Hamiltonian)::Dims = tuple(H.dim1, fill(H.s.N, H.s.d * (H.s.n - 2))...)
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"Apply 'H' on 'v' and store the result in 'out' using the 'cpu_tensor' backend"
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function LinearAlgebra.mul!(out::Array{Complex{T}}, H::Hamiltonian{T}, v::Array{Complex{T}})::Array{Complex{T}} where {T<:Float}
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@ -47,18 +52,23 @@ function LinearAlgebra.mul!(out::Array{Complex{T}}, H::Hamiltonian{T}, v::Array{
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for dim = 1:H.s.d
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for coord1 = 1:coords
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for coord2 = 1:coord1
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i1 = which_index(H.s, dim, coord1)
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i2 = which_index(H.s, dim, coord2)
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nconList_1 = [-i1, 1]
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nconList_2 = [-i2, 2]
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nconList_v = copy(nconList_v_template)
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if i1 == i2
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nconList_2[1] = 1
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if coord1 == 1 && coord2 == 1
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else
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nconList_v[i1] = 1
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i1 = which_index(H.s, dim, coord1)
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i2 = which_index(H.s, dim, coord2)
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nconList_1 = [-i1, 1]
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nconList_2 = [-i2, 2]
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nconList_v = copy(nconList_v_template)
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if i1 == i2
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nconList_2[1] = 1
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else
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nconList_v[i1] = 1
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end
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nconList_v[i2] = 2
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v_new = @ncon((H.K_partial, H.K_partial, v), (nconList_1, nconList_2, nconList_v))
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end
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nconList_v[i2] = 2
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v_new = @ncon((H.K_partial, H.K_partial, v), (nconList_1, nconList_2, nconList_v))
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out = axpy!(1, v_new, out)
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end
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end
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39
common.jl
39
common.jl
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@ -1,4 +1,7 @@
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include("irrep.jl")
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Float = Union{Float32,Float64}
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@enum rep all A1
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"A few-body system defined by its physical parameters"
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struct system{T}
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@ -8,7 +11,22 @@ struct system{T}
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L::T
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μ::T
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system{T}(d::Int, n::Int, N::Int, L::Real, μ::Real=0.5) where {T<:Float} = new{T}(d, n, N, convert(T, L), convert(T, μ))
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sym::rep
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unique_i::Array{Int}
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unique_point::Array{Int}
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multiplicity::Array{Int}
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function system{T}(d::Int, n::Int, N::Int, L::Real, μ::Real=0.5, sym::rep=all) where {T<:Float}
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@assert d == 3 "Only supports 3D"
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if sym == all
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unique_i, unique_point, multiplicity = calculate_all_data(N)
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elseif sym == A1
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unique_i, unique_point, multiplicity = calculate_A1_data(N)
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else
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throw(ArgumentError("Symmetry not yet implemented"))
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end
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return new{T}(d, n, N, convert(T, L), convert(T, μ), sym, unique_i, unique_point, multiplicity)
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end
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end
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norm_square(x::Array{Int})::Int = sum(x .* x)
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@ -23,18 +41,27 @@ function ∂_1DOF(s::system{T}, k::Int, l::Int)::Complex{T} where {T<:Float}
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end
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"Which index (dimension of the multidimensional array) corresponds to spatial dimension 'dim' and particle 'p'?"
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which_index(s::system, dim::Int, p::Int)::Int = (dim - 1) * (s.n - 1) + p
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which_index(s::system, dim::Int, p::Int)::Int = (dim - 1) * (s.n - 2) + p + 1
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"Δk (distance in terms of lattice paramter) between two particles along the given dimension"
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function get_k(s::system, i::CartesianIndex, dim::Int, p::Int)::Int
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if p == 1
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s.unique_point[i[1], dim]
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else
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return i[which_index(s, dim, p)] - s.N ÷ 2 - 1
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end
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end
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"Δk (distance in terms of lattice paramter) between two particles along the given dimension"
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function get_Δk(s::system, i::CartesianIndex, dim::Int, p1::Int, p2::Int)::Int
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if p1 == p2
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return 0
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elseif p1 == s.n
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return -(i[which_index(s, dim, p2)] - s.N ÷ 2 - 1)
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return -get_k(s, i, dim, p2)
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elseif p2 == s.n
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return i[which_index(s, dim, p1)] - s.N ÷ 2 - 1
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return get_k(s, i, dim, p1)
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else
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return i[which_index(s, dim, p1)] - i[which_index(s, dim, p2)]
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return get_k(s, i, dim, p1) - get_k(s, i, dim, p2)
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end
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end
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@ -42,7 +69,7 @@ end
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function calculate_Vs(s::system{T}, V_twobody::Function, ϕ::T, n_image::Int)::Array{Complex{T}} where {T<:Float}
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coeff² = (exp(im * ϕ) * s.L / s.N)^2
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images = collect.(Iterators.product(fill(-n_image:n_image, s.d)...)) # TODO: Learn how to use tuples instead of vectors
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Vs = zeros(Complex{T}, fill(s.N, s.d * (s.n - 1))...)
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Vs = zeros(Complex{T}, length(s.unique_i), fill(s.N, s.d * (s.n - 2))...)
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Threads.@threads for i in CartesianIndices(Vs)
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for p1 in 1:s.n
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for p2 in (p1 + 1):s.n
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56
irrep.jl
56
irrep.jl
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@ -1,9 +1,18 @@
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using DelimitedFiles
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rotations = readdlm("rotations.mat", ',', Int, '\n')
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rotations = reshape(rotations, (24, 3, 3))
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using DelimitedFiles, LinearAlgebra, StatsBase
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function get_A1_labels(N::Int)
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rotations = readdlm("rotations.csv", ',', Int, '\n')
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function calculate_all_data(N::Int)
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ks = -N÷2:N÷2-1
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lattice = hcat((collect.(Iterators.product(ks, ks, ks)))...)
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unique_i = collect(1:N^3)
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multiplicity = fill(1, length(unique_i))
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unique_point = transpose(lattice)
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return unique_i, unique_point, multiplicity
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end
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function calculate_A1_data(N::Int)
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rotations = readdlm("rotations.mat", ',', Int, '\n')
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rotations = reshape(rotations, (24, 3, 3))
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ks = -N÷2:N÷2-1
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@ -25,9 +34,42 @@ function get_A1_labels(N::Int)
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end
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end
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return labels
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unique_i = unique(labels)
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multiplicity = countmap(labels)
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unique_point = transpose(lattice[unique_i, :])
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return unique_i, unique_point, multiplicity
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end
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function sym_reduce(N::Int, K_full)
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function sym_reduce(s, K_partial)
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I = one(K_partial)
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K_partial_x = kron(kron(K_partial, I), I)
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K_partial_y = kron(kron(I, K_partial), I)
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K_partial_z = kron(kron(I, I), K_partial)
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# for s in 1:N^3
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# if labels[s] != s
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# for mat in (K_partial_x, K_partial_y, K_partial_z)
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# mat[labels[s], :] += mat[s, :]
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# mat[s, :] = 0
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# mat[:, labels[s]] += mat[:, s]
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# mat[:, s] = 0
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# end
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# end
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# end
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for i in s.unique_i
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K_partial_x[i, :] *= s.multiplicity[i]
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K_partial_x[:, i] *= s.multiplicity[i]
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K_partial_y[i, :] *= s.multiplicity[i]
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K_partial_y[:, i] *= s.multiplicity[i]
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K_partial_z[i, :] *= s.multiplicity[i]
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K_partial_z[:, i] *= s.multiplicity[i]
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end
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K_partial_x = K_partial_x[s.unique_i, s.unique_i]
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K_partial_y = K_partial_y[s.unique_i, s.unique_i]
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K_partial_z = K_partial_z[s.unique_i, s.unique_i]
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return K_partial_x, K_partial_y, K_partial_z
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end
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@ -0,0 +1,49 @@
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"include(\"Hamiltonian.jl\")\n",
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"\n",
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"println(\"Running with \",Threads.nthreads(),\" thread(s)\")\n",
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"\n",
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"T=Float32\n",
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"\n",
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"function V_test(r2)\n",
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" return -4*exp(-r2/4)\n",
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"end\n",
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"\n",
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"n = 2\n",
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"N = 16\n",
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"println(\"\\n$n-body system with N=$N\")\n",
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"\n",
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"for L::T in 5.0:9.0\n",
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" print(\"L=$L\")\n",
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" s=system{T}(3,n,N,L,0.5,all)\n",
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" @time H=Hamiltonian{T}(s,V_test,0,0,cpu_tensor)\n",
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" #evals,_,_ = eig(H,5)\n",
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" #println(real.(evals))\n",
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"end"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 1.9.0",
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"language": "julia",
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"name": "julia-1.9"
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},
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"language_info": {
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"file_extension": ".jl",
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"mimetype": "application/julia",
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"name": "julia",
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"version": "1.9.0"
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},
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"orig_nbformat": 4
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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