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eigen_heisenberg.jl
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### A Pluto.jl notebook ###
# v0.19.22
using Markdown
using InteractiveUtils
# ╔═╡ f96a43bc-bdad-11ed-208a-a72f92027f33
using Yao,YaoPlots, Plots, JLD2, LinearAlgebra
# ╔═╡ 2e230d67-5d92-4e52-a923-2bfd1c17b4cc
"""
hamiltonian(nbit::Int, periodic::Bool=true)
1D Heisenberg hamiltonian with Dzyaloshinkii-Moriya and random-field
"""
function hamiltonian(nbit::Int,W ; periodic::Bool=true)
sx = i -> put(nbit, i=>X)
sy = i -> put(nbit, i=>Y)
sz = i -> put(nbit, i=>Z)
hopping_term = map(1:(periodic ? nbit : nbit-1)) do i
j = i%nbit + 1
sx(i)*sx(j)+sy(i)*sy(j)+sz(i)*sz(j) + sy(i)*sz(j) - sz(i)*sy(j) -sx(i)*sz(j) + sz(i)*sx(j) + sx(i)*sy(j) - sy(i)*sx(j)
end |> sum
Wi = rand(-W:.001:W, nbit)
disorder = map(1:nbit) do i
Wi[i] * sx(i)
end |> sum
hopping_term + disorder
end
# ╔═╡ f73730c4-a3f6-4997-a4f9-123cd55cd404
typeof(X)
# ╔═╡ 4d069a57-32e6-40d7-88f2-f881fc3fa0b1
function my_ising(nbit::Int, h; periodic::Bool=true)
hopping = map(1:(periodic ? nbit : nbit-1)) do i
repeat(nbit, X, (i, i%nbit+1))
end |> sum
hopping + h*sum(map(i->put(nbit, i=>X), 1:nbit))
end
# ╔═╡ 72d0eb91-6a83-437a-a2ad-ef4a7a30f1e8
"""
1D heisenberg model with random-field
"""
function heisenberg_randfield(nbit::Int, W ; periodic::Bool=true)
sx = i -> put(nbit, i => X)
hopping = map(1:(periodic ? nbit : nbit-1)) do i
j=i%nbit+1
repeat(nbit,X,(i,j)) + repeat(nbit, Y, (i,j)) + repeat(nbit, Z, (i,j))
end |> sum
Wi = rand(-W:.001:W, nbit)
disorder = map(1:nbit) do i
Wi[i] * sx(i)
end |> sum
hopping + disorder
end
# ╔═╡ 02c1f7fb-057d-4641-aa3d-24260712a3b9
function transverse_ising(nbit::Int, h::Number; periodic::Bool=true)
ising_term = map(1:(periodic ? nbit : nbit-1)) do i
repeat(nbit,Z,(i,i%nbit+1))
end |> sum
ising_term + h*sum(map(i->put(nbit,i=>X), 1:nbit))
end
# ╔═╡ 58fcd024-02da-48f6-909d-5ac664742b7b
# ╠═╡ disabled = true
#=╠═╡
elists = [ eigvals(Matrix(mat(transverse_ising(14,h;periodic=false)))) for h in 0:0.01:40]
╠═╡ =#
# ╔═╡ 64d5992c-3588-4402-a477-2e61999e274e
# ╠═╡ disabled = true
#=╠═╡
length(0:0.01:1)
╠═╡ =#
# ╔═╡ dbdd4718-8f07-4a88-96f6-d186fa2879d6
# ╠═╡ disabled = true
#=╠═╡
# elist for the top 15 energy
ePlotlists = [map(i -> (elists[i][j]-elists[i][1]), 1:201) for j in 1:15]
╠═╡ =#
# ╔═╡ af9a3e30-a35d-49bb-ba87-31dc9cb64872
# ╠═╡ disabled = true
#=╠═╡
# Plot energy band
Plots.scatter(0:.01:2, ePlotlists,ms=0.5,legend=:outertopright)
╠═╡ =#
# ╔═╡ c36da86e-94ea-4b88-956e-0aeb3f7ed75b
#=╠═╡
maxvar = i -> maximum(map(j -> elists[i][j+1] - elists[i][j], 1:1023))
╠═╡ =#
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
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YaoPlots = "32cfe2d9-419e-45f2-8191-2267705d8dbc"
[compat]
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"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
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