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Update Ising dqpt example
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lkdvos committed Jan 22, 2025
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57 changes: 25 additions & 32 deletions docs/src/examples/quantum1d/3.ising-dqpt/index.md
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Original file line number Diff line number Diff line change
Expand Up @@ -32,22 +32,21 @@ For those ``g`` we expect non-analicities to occur at ``t_n ≈ 2.35 (n + 1/2)``
First we construct the hamiltonian in mpo form, and obtain the pre-quenched groundstate:

````julia
H₀ = transverse_field_ising(; g=-0.5)

L = 20
ψ₀ = FiniteMPS(rand, ComplexF64, L, ℂ^2, ℂ^10)
H₀ = transverse_field_ising(FiniteChain(L); g=-0.5)
ψ₀ = FiniteMPS(L, ℂ^2, ℂ^10)
ψ₀, _ = find_groundstate(ψ₀, H₀, DMRG());
````

````
[ Info: DMRG init: obj = +9.799964091770e+00 err = 1.5223e-01
[ Info: DMRG 1: obj = -2.040021714743e+01 err = 2.4038839149e-02 time = 0.09 sec
[ Info: DMRG 2: obj = -2.040021715170e+01 err = 6.0313575856e-07 time = 0.07 sec
[ Info: DMRG 3: obj = -2.040021773534e+01 err = 1.6799456960e-05 time = 0.14 sec
[ Info: DMRG 4: obj = -2.040021786694e+01 err = 1.9058246307e-06 time = 0.09 sec
[ Info: DMRG 5: obj = -2.040021786703e+01 err = 1.1474711603e-06 time = 0.05 sec
[ Info: DMRG 6: obj = -2.040021786703e+01 err = 4.3837579221e-10 time = 0.02 sec
[ Info: DMRG conv 7: obj = -2.040021786703e+01 err = 1.9834477158e-11 time = 0.50 sec
[ Info: DMRG init: obj = +1.002387808585e+01 err = 1.4432e-01
[ Info: DMRG 1: obj = -2.040021714927e+01 err = 4.0939235067e-03 time = 0.07 sec
[ Info: DMRG 2: obj = -2.040021715177e+01 err = 4.1045749328e-07 time = 0.02 sec
[ Info: DMRG 3: obj = -2.040021782419e+01 err = 4.0893119931e-05 time = 0.11 sec
[ Info: DMRG 4: obj = -2.040021786700e+01 err = 1.5231059570e-06 time = 0.12 sec
[ Info: DMRG 5: obj = -2.040021786703e+01 err = 1.1927466419e-07 time = 0.04 sec
[ Info: DMRG 6: obj = -2.040021786703e+01 err = 1.0958548921e-10 time = 0.02 sec
[ Info: DMRG conv 7: obj = -2.040021786703e+01 err = 2.1531775493e-12 time = 0.43 sec
````

Expand All @@ -63,7 +62,7 @@ echo(ψ₀::FiniteMPS, ψₜ::FiniteMPS) = -2 * log(abs(dot(ψ₀, ψₜ))) / le
We will initially use a two-site TDVP scheme to dynamically increase the bond dimension while time evolving, and later on switch to a faster one-site scheme. A single timestep can be done using

````julia
H₁ = transverse_field_ising(; g=-2.0)
H₁ = transverse_field_ising(FiniteChain(L); g=-2.0)
ψₜ = deepcopy(ψ₀)
dt = 0.01
ψₜ, envs = timestep(ψₜ, H₁, 0, dt, TDVP2(; trscheme=truncdim(20)));
Expand All @@ -75,9 +74,11 @@ Putting it all together, we get

````julia
function finite_sim(L; dt=0.05, finaltime=5.0)
ψ₀ = FiniteMPS(rand, ComplexF64, L, ℂ^2, ℂ^10)
ψ₀ = FiniteMPS(L, ℂ^2, ℂ^10)
H₀= transverse_field_ising(FiniteChain(L); g=-0.5)
ψ₀, _ = find_groundstate(ψ₀, H₀, DMRG())

H₁ = transverse_field_ising(FiniteChain(L); g=-2.0)
ψₜ = deepcopy(ψ₀)
envs = environments(ψₜ, H₁)

Expand Down Expand Up @@ -106,27 +107,18 @@ Similarly we could start with an initial infinite state and find the pre-quench

````julia
ψ₀ = InfiniteMPS([ℂ^2], [ℂ^10])
H₀ = transverse_field_ising(; g=-0.5)
ψ₀, _ = find_groundstate(ψ₀, H₀, VUMPS());
````

````
[ Info: VUMPS init: obj = +5.000419382862e-01 err = 3.8507e-01
[ Info: VUMPS 1: obj = -1.062780898337e+00 err = 2.4151374798e-02 time = 1.31 sec
┌ Warning: ignoring imaginary component -3.817802691569172e-6 from total weight 2.4343214394239743: operator might not be hermitian?
│ α = 1.7081089443203243 - 3.817802691569172e-6im
│ β₁ = 0.14004438155194618
│ β₂ = 1.7287776826281838
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
┌ Warning: ignoring imaginary component -4.33258309393697e-6 from total weight 3.290563788912538: operator might not be hermitian?
│ α = 2.784222669687663 - 4.33258309393697e-6im
│ β₁ = 0.13141322180957496
│ β₂ = 1.7488981501547187
└ @ KrylovKit ~/.julia/packages/KrylovKit/xccMN/src/factorizations/lanczos.jl:170
[ Info: VUMPS 2: obj = -1.063544409753e+00 err = 1.4337063091e-05 time = 0.08 sec
[ Info: VUMPS 3: obj = -1.063544409973e+00 err = 1.7048015038e-07 time = 0.01 sec
[ Info: VUMPS 4: obj = -1.063544409973e+00 err = 1.7183182449e-08 time = 0.01 sec
[ Info: VUMPS 5: obj = -1.063544409973e+00 err = 5.8865202016e-10 time = 0.01 sec
[ Info: VUMPS conv 6: obj = -1.063544409973e+00 err = 6.8020365686e-11 time = 1.42 sec
[ Info: VUMPS init: obj = +4.829091166942e-01 err = 3.8333e-01
[ Info: VUMPS 1: obj = -1.062402142520e+00 err = 2.6498065851e-02 time = 0.02 sec
[ Info: VUMPS 2: obj = -1.063544409278e+00 err = 2.4370573433e-05 time = 0.01 sec
[ Info: VUMPS 3: obj = -1.063544409973e+00 err = 1.2541001144e-07 time = 0.01 sec
[ Info: VUMPS 4: obj = -1.063544409973e+00 err = 2.2271390880e-09 time = 0.01 sec
[ Info: VUMPS 5: obj = -1.063544409973e+00 err = 1.3003499540e-10 time = 0.01 sec
[ Info: VUMPS conv 6: obj = -1.063544409973e+00 err = 1.2478380148e-11 time = 0.08 sec
````

Expand All @@ -138,7 +130,7 @@ dot(ψ₀, ψ₀)
````

````
1.0000000000000018 - 7.06078012856404e-16im
1.0000000000000004 + 1.6174779448250835e-16im
````

so the loschmidth echo takes on the pleasant form
Expand All @@ -155,6 +147,7 @@ Growing the bond dimension by ``5`` can be done by calling:

````julia
ψₜ = deepcopy(ψ₀)
H₁ = transverse_field_ising(; g=-2.0)
ψₜ, envs = changebonds(ψₜ, H₁, OptimalExpand(; trscheme=truncdim(5)));
````

Expand Down Expand Up @@ -183,7 +176,7 @@ function infinite_sim(dt=0.05, finaltime=5.0)
if t < 50dt # if t is sufficiently small, we increase the bond dimension
ψₜ, envs = changebonds(ψₜ, H₁, OptimalExpand(; trscheme=truncdim(1)), envs)
end
(ψₜ, envs) = timestep(ψₜ, H₁, 0, dt, TDVP(), envs)
ψₜ, envs = timestep(ψₜ, H₁, 0, dt, TDVP(), envs)
push!(echos, echo(ψₜ, ψ₀))
end

Expand Down
19 changes: 11 additions & 8 deletions docs/src/examples/quantum1d/3.ising-dqpt/main.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -44,10 +44,9 @@
"outputs": [],
"cell_type": "code",
"source": [
"H₀ = transverse_field_ising(; g=-0.5)\n",
"\n",
"L = 20\n",
"ψ₀ = FiniteMPS(rand, ComplexF64, L, ℂ^2, ℂ^10)\n",
"H₀ = transverse_field_ising(FiniteChain(L); g=-0.5)\n",
"ψ₀ = FiniteMPS(L, ℂ^2, ℂ^10)\n",
"ψ₀, _ = find_groundstate(ψ₀, H₀, DMRG());"
],
"metadata": {},
Expand Down Expand Up @@ -83,7 +82,7 @@
"outputs": [],
"cell_type": "code",
"source": [
"H₁ = transverse_field_ising(; g=-2.0)\n",
"H₁ = transverse_field_ising(FiniteChain(L); g=-2.0)\n",
"ψₜ = deepcopy(ψ₀)\n",
"dt = 0.01\n",
"ψₜ, envs = timestep(ψₜ, H₁, 0, dt, TDVP2(; trscheme=truncdim(20)));"
Expand All @@ -105,9 +104,11 @@
"cell_type": "code",
"source": [
"function finite_sim(L; dt=0.05, finaltime=5.0)\n",
" ψ₀ = FiniteMPS(rand, ComplexF64, L, ℂ^2, ℂ^10)\n",
" ψ₀ = FiniteMPS(L, ℂ^2, ℂ^10)\n",
" H₀= transverse_field_ising(FiniteChain(L); g=-0.5)\n",
" ψ₀, _ = find_groundstate(ψ₀, H₀, DMRG())\n",
"\n",
" H₁ = transverse_field_ising(FiniteChain(L); g=-2.0)\n",
" ψₜ = deepcopy(ψ₀)\n",
" envs = environments(ψₜ, H₁)\n",
"\n",
Expand Down Expand Up @@ -147,6 +148,7 @@
"cell_type": "code",
"source": [
"ψ₀ = InfiniteMPS([ℂ^2], [ℂ^10])\n",
"H₀ = transverse_field_ising(; g=-0.5)\n",
"ψ₀, _ = find_groundstate(ψ₀, H₀, VUMPS());"
],
"metadata": {},
Expand Down Expand Up @@ -201,6 +203,7 @@
"cell_type": "code",
"source": [
"ψₜ = deepcopy(ψ₀)\n",
"H₁ = transverse_field_ising(; g=-2.0)\n",
"ψₜ, envs = changebonds(ψₜ, H₁, OptimalExpand(; trscheme=truncdim(5)));"
],
"metadata": {},
Expand Down Expand Up @@ -249,7 +252,7 @@
" if t < 50dt # if t is sufficiently small, we increase the bond dimension\n",
" ψₜ, envs = changebonds(ψₜ, H₁, OptimalExpand(; trscheme=truncdim(1)), envs)\n",
" end\n",
" (ψₜ, envs) = timestep(ψₜ, H₁, 0, dt, TDVP(), envs)\n",
" ψₜ, envs = timestep(ψₜ, H₁, 0, dt, TDVP(), envs)\n",
" push!(echos, echo(ψₜ, ψ₀))\n",
" end\n",
"\n",
Expand Down Expand Up @@ -282,11 +285,11 @@
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.1"
"version": "1.11.2"
},
"kernelspec": {
"name": "julia-1.11",
"display_name": "Julia 1.11.1",
"display_name": "Julia 1.11.2",
"language": "julia"
}
},
Expand Down
1 change: 1 addition & 0 deletions examples/Cache.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -3,4 +3,5 @@

[quantum1d]
"2.haldane" = "4f3e177a30df907cf7b9a47958ddf97741e4d0398ae1876e0f4977ccb93ae651"
"3.ising-dqpt" = "f437ac4560db51f67e3997867c02bb8844b1077731b1dd1a06c61ab7c4846e97"
"1.ising-cft" = "bd1253451973aa73c4fee6b64d81ee52cc2feba5b9632f87ce332eea3a05f460"
14 changes: 9 additions & 5 deletions examples/quantum1d/3.ising-dqpt/main.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -25,10 +25,10 @@ For those ``g`` we expect non-analicities to occur at ``t_n ≈ 2.35 (n + 1/2)``
First we construct the hamiltonian in mpo form, and obtain the pre-quenched groundstate:
"""

H₀ = transverse_field_ising(; g=-0.5)

L = 20
ψ₀ = FiniteMPS(rand, ComplexF64, L, ℂ^2, ℂ^10)
H₀ = transverse_field_ising(FiniteChain(L); g=-0.5)
ψ₀ = FiniteMPS(L, ℂ^2, ℂ^10)
ψ₀, _ = find_groundstate(ψ₀, H₀, DMRG());

md"""
Expand All @@ -44,7 +44,7 @@ md"""
We will initially use a two-site TDVP scheme to dynamically increase the bond dimension while time evolving, and later on switch to a faster one-site scheme. A single timestep can be done using
"""

H₁ = transverse_field_ising(; g=-2.0)
H₁ = transverse_field_ising(FiniteChain(L); g=-2.0)
ψₜ = deepcopy(ψ₀)
dt = 0.01
ψₜ, envs = timestep(ψₜ, H₁, 0, dt, TDVP2(; trscheme=truncdim(20)));
Expand All @@ -56,9 +56,11 @@ Putting it all together, we get
"""

function finite_sim(L; dt=0.05, finaltime=5.0)
ψ₀ = FiniteMPS(rand, ComplexF64, L, ℂ^2, ℂ^10)
ψ₀ = FiniteMPS(L, ℂ^2, ℂ^10)
H₀= transverse_field_ising(FiniteChain(L); g=-0.5)
ψ₀, _ = find_groundstate(ψ₀, H₀, DMRG())

H₁ = transverse_field_ising(FiniteChain(L); g=-2.0)
ψₜ = deepcopy(ψ₀)
envs = environments(ψₜ, H₁)

Expand All @@ -83,6 +85,7 @@ Similarly we could start with an initial infinite state and find the pre-quench
"""

ψ₀ = InfiniteMPS([ℂ^2], [ℂ^10])
H₀ = transverse_field_ising(; g=-0.5)
ψ₀, _ = find_groundstate(ψ₀, H₀, VUMPS());

md"""
Expand All @@ -107,6 +110,7 @@ Growing the bond dimension by ``5`` can be done by calling:
"""

ψₜ = deepcopy(ψ₀)
H₁ = transverse_field_ising(; g=-2.0)
ψₜ, envs = changebonds(ψₜ, H₁, OptimalExpand(; trscheme=truncdim(5)));

# a single timestep is easy
Expand All @@ -133,7 +137,7 @@ function infinite_sim(dt=0.05, finaltime=5.0)
if t < 50dt # if t is sufficiently small, we increase the bond dimension
ψₜ, envs = changebonds(ψₜ, H₁, OptimalExpand(; trscheme=truncdim(1)), envs)
end
(ψₜ, envs) = timestep(ψₜ, H₁, 0, dt, TDVP(), envs)
ψₜ, envs = timestep(ψₜ, H₁, 0, dt, TDVP(), envs)
push!(echos, echo(ψₜ, ψ₀))
end

Expand Down

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