74 lines
2.4 KiB
Julia
74 lines
2.4 KiB
Julia
using LinearAlgebra, SparseArrays, Arpack
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include("helper.jl")
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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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target = 4.0766890719636875 - 0.012758927741074495im
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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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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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# generate Berggren bases
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@time "berg_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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to_berg_basis(mat, j) = transpose(berg_bases[1 + j] .* ws) * mat * berg_bases[1 + j]
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end
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@time "U_berggren" begin
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U_blocks = [kron(berg_bases[1 + j1], berg_bases[1 + j2]) for (j1, j2) in js]
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U = blockdiag(sparse.(U_blocks)...)
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end
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@time "Block diagonal part" begin
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Hb_blocks = [kron_sum(to_berg_basis(get_H_matrix((k, kp) -> V_l(j1, k, kp), ks, ws, μ), j1), to_berg_basis(get_H_matrix((k, kp) -> V_l(j2, k, kp), ks, ws, μ), j2)) for (j1, j2) in js]
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Hb = blockdiag(sparse.(Hb_blocks)...)
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end
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@time "T_cross" T_cross = get_2p_p1p2_matrix(length(ks), js, Λ, berg_bases, berg_bases, ws) ./ (2*μ)
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E_max = 30
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μω_global = 0.5
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# due to simple relative coordinates
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μω = μω_global * 2
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μ = m/2
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@time "V12_HO" V12_HO = get_src_V12_matrix(V_of_r, E_max, Λ, μω_global; atol=10^-6, maxevals=10^5)
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@time "W" W = get_W_matrix(basis, E_max, Λ, μω, μω; weights=true)
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@time "V12_p" V12_p = W * V12_HO * transpose(W)
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@time "V12" V12 = transpose(U) * V12_p * U
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@time "H" H = Hb + T_cross + V12
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@time "Eigenvalues" evals, _ = eigs(H, sigma=target, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
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display(evals)
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