58 lines
2.0 KiB
Julia
58 lines
2.0 KiB
Julia
using LinearAlgebra, SparseArrays, Plots
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include("../p_space.jl")
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include("../ho_basis.jl")
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include("../berggren.jl")
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println("No of threads = ", Threads.nthreads())
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atol = 10^-5
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maxevals = 10^5
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R_cutoff = 16
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Λ = 0
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m = 1.0
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μ = m/2 # due to simple relative coordinates
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vertices = [0, 2 - 0.2im, 3, 4]
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subdivisions = [15, 10, 10]
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ks, ws = get_mesh(vertices, subdivisions)
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jmax = 4
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tri((j1, j2)) = triangle_ineq(j1, j2, Λ)
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js = collect(Iterators.filter(tri, iter_prod(0:jmax, 0:jmax)))
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basis = iter_prod(js, zip(ks, ws), zip(ks, ws)) # basis = ((j1, j2), (k1, w1), (k2, w2))
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basis_size = length(js) * length(ks)^2
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@assert length(basis) == basis_size "Something wrong with the basis"
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println("Basis size = $basis_size")
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V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
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V_l(j, k, kp) = Vl_mat_elem(V_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
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# generate p-space bases (actually identity matrices)
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@time "p-space bases" ps_bases = [Matrix(spdiagm(1 ./ sqrt.(ws))) for _ in 0:jmax]
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# generate Berggren bases
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@time "Berggren bases" begin
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berg_bases = Vector{Matrix{ComplexF64}}(undef, jmax + 1)
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for j in 0:jmax
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_, berg_basis = eigen(get_H_matrix((k, kp) -> V_l(j, k, kp), ks, ws, μ); permute=false, scale=false)
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N_berg = sum(berg_basis.^2 .* ws, dims=1)
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berg_bases[1 + j] = berg_basis ./ transpose(sqrt.(N_berg))
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end
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end
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@time "BB tranform matrix" begin
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U_blocks = [kron(berg_bases[1 + j1] .* ws, berg_bases[1 + j2] .* ws) for (j1, j2) in js]
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U = blockdiag(sparse.(U_blocks)...)
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end
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@time "In p-space" T_cross_PS = get_2p_p1p2_matrix(length(ks), js, Λ, ps_bases, ps_bases, ws)
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@time "In BB" T_cross_BB = get_2p_p1p2_matrix(length(ks), js, Λ, berg_bases, berg_bases, ws)
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@time "Basis transform" T_cross_transformed = transpose(U) * T_cross_PS * U
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diff = abs.(T_cross_transformed .- T_cross_BB)
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println("Max error = $(maximum(diff))")
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#@time "In in HO" T_cross_HO = get_2p_p1p2_matrix(n1s, l1s, n2s, l2s, Λ, μω, μω; dtype=ComplexF64)
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