{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Gross-Pitaevskii equation with magnetism"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"We solve the 2D Gross-Pitaevskii equation with a magnetic field.\n",
"This is similar to the\n",
"previous example (Gross-Pitaevskii equation in one dimension),\n",
"but with an extra term for the magnetic field.\n",
"We reproduce here the results of https://arxiv.org/pdf/1611.02045.pdf Fig. 10"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using DFTK\n",
"using StaticArrays\n",
"using Plots"
],
"metadata": {},
"execution_count": 1
},
{
"cell_type": "markdown",
"source": [
"Unit cell. Having one of the lattice vectors as zero means a 2D system"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"a = 15\n",
"lattice = a .* [[1 0 0.]; [0 1 0]; [0 0 0]];"
],
"metadata": {},
"execution_count": 2
},
{
"cell_type": "markdown",
"source": [
"Confining scalar potential, and magnetic vector potential"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"pot(x, y, z) = ((x - a/2)^2 + (y - a/2)^2)/2\n",
"ω = .6\n",
"Apot(x, y, z) = ω * @SVector [y - a/2, -(x - a/2), 0]\n",
"Apot(X) = Apot(X...);"
],
"metadata": {},
"execution_count": 3
},
{
"cell_type": "markdown",
"source": [
"Parameters"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"Ecut = 20 # Increase this for production\n",
"η = 500\n",
"C = η/2\n",
"α = 2\n",
"n_electrons = 1; # Increase this for fun"
],
"metadata": {},
"execution_count": 4
},
{
"cell_type": "markdown",
"source": [
"Collect all the terms, build and run the model"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iter Function value Gradient norm \n",
" 0 3.181378e+01 9.870895e+00\n",
" * time: 0.002177000045776367\n",
" 1 3.011008e+01 5.567599e+00\n",
" * time: 0.009013891220092773\n",
" 2 2.139950e+01 5.593874e+00\n",
" * time: 0.016654014587402344\n",
" 3 1.657827e+01 5.224965e+00\n",
" * time: 0.025249004364013672\n",
" 4 1.182497e+01 1.876204e+00\n",
" * time: 0.033312082290649414\n",
" 5 1.138761e+01 2.659294e+00\n",
" * time: 0.03926205635070801\n",
" 6 1.062140e+01 1.972147e+00\n",
" * time: 0.04570603370666504\n",
" 7 9.893499e+00 1.547767e+00\n",
" * time: 0.05213308334350586\n",
" 8 9.400374e+00 1.540797e+00\n",
" * time: 0.05857110023498535\n",
" 9 8.960376e+00 1.600791e+00\n",
" * time: 0.06446599960327148\n",
" 10 8.630369e+00 1.027981e+00\n",
" * time: 0.07117009162902832\n",
" 11 8.405594e+00 9.925518e-01\n",
" * time: 0.07755708694458008\n",
" 12 8.215028e+00 8.771012e-01\n",
" * time: 0.08423399925231934\n",
" 13 8.060957e+00 4.831716e-01\n",
" * time: 0.09109807014465332\n",
" 14 7.957614e+00 3.230127e-01\n",
" * time: 0.09706807136535645\n",
" 15 7.952174e+00 8.246058e-01\n",
" * time: 0.10203289985656738\n",
" 16 7.905007e+00 4.635742e-01\n",
" * time: 0.10765290260314941\n",
" 17 7.869904e+00 6.323642e-01\n",
" * time: 0.11279606819152832\n",
" 18 7.831834e+00 3.503089e-01\n",
" * time: 0.11961007118225098\n",
" 19 7.816516e+00 5.582323e-01\n",
" * time: 0.12477898597717285\n",
" 20 7.792292e+00 4.536573e-01\n",
" * time: 0.13014507293701172\n",
" 21 7.772558e+00 3.802472e-01\n",
" * time: 0.13544201850891113\n",
" 22 7.758859e+00 3.578391e-01\n",
" * time: 0.16525697708129883\n",
" 23 7.754024e+00 4.120638e-01\n",
" * time: 0.1685628890991211\n",
" 24 7.747321e+00 2.915412e-01\n",
" * time: 0.1733410358428955\n",
" 25 7.739785e+00 3.960328e-01\n",
" * time: 0.1766510009765625\n",
" 26 7.721315e+00 2.372297e-01\n",
" * time: 0.18109989166259766\n",
" 27 7.709032e+00 2.379223e-01\n",
" * time: 0.18420791625976562\n",
" 28 7.699102e+00 2.837649e-01\n",
" * time: 0.18744611740112305\n",
" 29 7.695808e+00 3.102473e-01\n",
" * time: 0.19069695472717285\n",
" 30 7.687183e+00 1.700968e-01\n",
" * time: 0.1947329044342041\n",
" 31 7.685180e+00 2.682569e-01\n",
" * time: 0.19808697700500488\n",
" 32 7.682984e+00 2.788849e-01\n",
" * time: 0.20148801803588867\n",
" 33 7.681360e+00 2.073162e-01\n",
" * time: 0.20453906059265137\n",
" 34 7.676597e+00 1.486242e-01\n",
" * time: 0.20862197875976562\n",
" 35 7.675333e+00 2.699651e-01\n",
" * time: 0.2120680809020996\n",
" 36 7.670708e+00 1.214227e-01\n",
" * time: 0.21514892578125\n",
" 37 7.665404e+00 1.318785e-01\n",
" * time: 0.2186110019683838\n",
" 38 7.662817e+00 1.001011e-01\n",
" * time: 0.22221589088439941\n",
" 39 7.662399e+00 1.446876e-01\n",
" * time: 0.22524499893188477\n",
" 40 7.660194e+00 9.392956e-02\n",
" * time: 0.22931289672851562\n",
" 41 7.659141e+00 1.360469e-01\n",
" * time: 0.23276400566101074\n",
" 42 7.657224e+00 8.737660e-02\n",
" * time: 0.23969197273254395\n",
" 43 7.656074e+00 1.343965e-01\n",
" * time: 0.2451789379119873\n",
" 44 7.655046e+00 1.016003e-01\n",
" * time: 0.2507638931274414\n",
" 45 7.653713e+00 8.724650e-02\n",
" * time: 0.25696897506713867\n",
" 46 7.651396e+00 5.985730e-02\n",
" * time: 0.2655661106109619\n",
" 47 7.650100e+00 9.278837e-02\n",
" * time: 0.27536892890930176\n",
" 48 7.647707e+00 8.950711e-02\n",
" * time: 0.2822530269622803\n",
" 49 7.646759e+00 1.855564e-01\n",
" * time: 0.28871893882751465\n",
" 50 7.644808e+00 1.355937e-01\n",
" * time: 0.297713041305542\n",
" 51 7.642266e+00 8.816050e-02\n",
" * time: 0.30451202392578125\n",
" 52 7.641308e+00 1.127601e-01\n",
" * time: 0.30992889404296875\n",
" 53 7.639486e+00 1.175096e-01\n",
" * time: 0.3323080539703369\n",
" 54 7.638471e+00 1.849132e-01\n",
" * time: 0.3355588912963867\n",
" 55 7.638311e+00 1.498368e-01\n",
" * time: 0.3388819694519043\n",
" 56 7.636410e+00 1.020664e-01\n",
" * time: 0.3424839973449707\n",
" 57 7.634122e+00 1.214188e-01\n",
" * time: 0.3457679748535156\n",
" 58 7.632174e+00 9.744501e-02\n",
" * time: 0.348966121673584\n",
" 59 7.631657e+00 1.157391e-01\n",
" * time: 0.3522000312805176\n",
" 60 7.629865e+00 8.564354e-02\n",
" * time: 0.356442928314209\n",
" 61 7.628720e+00 6.129150e-02\n",
" * time: 0.35999011993408203\n",
" 62 7.627565e+00 7.484975e-02\n",
" * time: 0.3632240295410156\n",
" 63 7.626556e+00 5.450509e-02\n",
" * time: 0.3671300411224365\n",
" 64 7.626366e+00 1.247762e-01\n",
" * time: 0.37050700187683105\n",
" 65 7.626152e+00 1.165183e-01\n",
" * time: 0.37384510040283203\n",
" 66 7.625068e+00 6.049342e-02\n",
" * time: 0.3779571056365967\n",
" 67 7.624564e+00 9.068418e-02\n",
" * time: 0.38132810592651367\n",
" 68 7.623702e+00 8.241390e-02\n",
" * time: 0.38471293449401855\n",
" 69 7.623181e+00 1.032951e-01\n",
" * time: 0.3881070613861084\n",
" 70 7.622232e+00 4.799063e-02\n",
" * time: 0.3933279514312744\n",
" 71 7.621751e+00 5.852966e-02\n",
" * time: 0.3968479633331299\n",
" 72 7.621444e+00 6.514392e-02\n",
" * time: 0.4002671241760254\n",
" 73 7.621335e+00 5.034334e-02\n",
" * time: 0.4071919918060303\n",
" 74 7.620891e+00 5.019804e-02\n",
" * time: 0.4126110076904297\n",
" 75 7.620466e+00 4.222768e-02\n",
" * time: 0.4195590019226074\n",
" 76 7.620076e+00 2.615660e-02\n",
" * time: 0.4252490997314453\n",
" 77 7.619831e+00 3.308669e-02\n",
" * time: 0.42986202239990234\n",
" 78 7.619582e+00 2.643220e-02\n",
" * time: 0.43650293350219727\n",
" 79 7.619580e+00 5.961720e-02\n",
" * time: 0.4399290084838867\n",
" 80 7.619542e+00 4.142535e-02\n",
" * time: 0.4431760311126709\n",
" 81 7.619308e+00 3.200206e-02\n",
" * time: 0.4461050033569336\n",
" 82 7.619115e+00 6.132642e-02\n",
" * time: 0.449415922164917\n",
" 83 7.618842e+00 5.767187e-02\n",
" * time: 0.4529240131378174\n",
" 84 7.618754e+00 5.739387e-02\n",
" * time: 0.47153210639953613\n",
" 85 7.618407e+00 3.375749e-02\n",
" * time: 0.47493505477905273\n",
" 86 7.617922e+00 3.605143e-02\n",
" * time: 0.47808408737182617\n",
" 87 7.617403e+00 3.743774e-02\n",
" * time: 0.48122310638427734\n",
" 88 7.617212e+00 5.118934e-02\n",
" * time: 0.4925239086151123\n",
" 89 7.616759e+00 4.118817e-02\n",
" * time: 0.49580812454223633\n",
" 90 7.616357e+00 6.254198e-02\n",
" * time: 0.5002820491790771\n",
" 91 7.616030e+00 3.408293e-02\n",
" * time: 0.5042860507965088\n",
" 92 7.615747e+00 3.991483e-02\n",
" * time: 0.5073931217193604\n",
" 93 7.615607e+00 6.159236e-02\n",
" * time: 0.5106620788574219\n",
" 94 7.615289e+00 3.964765e-02\n",
" * time: 0.5148138999938965\n",
" 95 7.615028e+00 5.277666e-02\n",
" * time: 0.5178990364074707\n",
" 96 7.614550e+00 5.343814e-02\n",
" * time: 0.5211019515991211\n",
" 97 7.614191e+00 6.015162e-02\n",
" * time: 0.5243370532989502\n",
" 98 7.613900e+00 5.843907e-02\n",
" * time: 0.5274810791015625\n",
" 99 7.613731e+00 7.718938e-02\n",
" * time: 0.5312039852142334\n",
" 100 7.613350e+00 6.671927e-02\n",
" * time: 0.5343799591064453\n",
" 101 7.612989e+00 5.178083e-02\n",
" * time: 0.5383169651031494\n",
" 102 7.612718e+00 3.536126e-02\n",
" * time: 0.5424759387969971\n",
" 103 7.612420e+00 5.074594e-02\n",
" * time: 0.546929121017456\n",
" 104 7.612170e+00 5.592484e-02\n",
" * time: 0.5514869689941406\n",
" 105 7.612047e+00 4.115484e-02\n",
" * time: 0.5553591251373291\n",
" 106 7.611835e+00 3.714871e-02\n",
" * time: 0.5586891174316406\n",
" 107 7.611523e+00 3.073197e-02\n",
" * time: 0.5629539489746094\n",
" 108 7.611461e+00 4.808942e-02\n",
" * time: 0.5661389827728271\n",
" 109 7.611203e+00 3.648855e-02\n",
" * time: 0.5702519416809082\n",
" 110 7.610881e+00 3.144785e-02\n",
" * time: 0.5737159252166748\n",
" 111 7.610516e+00 4.533274e-02\n",
" * time: 0.5774860382080078\n",
" 112 7.610248e+00 4.137887e-02\n",
" * time: 0.5816209316253662\n",
" 113 7.610134e+00 3.941642e-02\n",
" * time: 0.5857090950012207\n",
" 114 7.609981e+00 1.991233e-02\n",
" * time: 0.6016309261322021\n",
" 115 7.609887e+00 3.678904e-02\n",
" * time: 0.6048579216003418\n",
" 116 7.609667e+00 3.054150e-02\n",
" * time: 0.6080119609832764\n",
" 117 7.609580e+00 3.545305e-02\n",
" * time: 0.6110310554504395\n",
" 118 7.609366e+00 3.374087e-02\n",
" * time: 0.6140389442443848\n",
" 119 7.609111e+00 2.132177e-02\n",
" * time: 0.6176400184631348\n",
" 120 7.608921e+00 3.232676e-02\n",
" * time: 0.6208279132843018\n",
" 121 7.608783e+00 5.344966e-02\n",
" * time: 0.6243560314178467\n",
" 122 7.608457e+00 3.736616e-02\n",
" * time: 0.6274220943450928\n",
" 123 7.608287e+00 4.028187e-02\n",
" * time: 0.6305899620056152\n",
" 124 7.608087e+00 4.563596e-02\n",
" * time: 0.6339280605316162\n",
" 125 7.607794e+00 3.031604e-02\n",
" * time: 0.6379690170288086\n",
" 126 7.607518e+00 3.119621e-02\n",
" * time: 0.6421329975128174\n",
" 127 7.607324e+00 2.486876e-02\n",
" * time: 0.6456940174102783\n",
" 128 7.607144e+00 3.927294e-02\n",
" * time: 0.6484870910644531\n",
" 129 7.606905e+00 3.743028e-02\n",
" * time: 0.6514968872070312\n",
" 130 7.606865e+00 5.001889e-02\n",
" * time: 0.6597630977630615\n",
" 131 7.606684e+00 5.998625e-02\n",
" * time: 0.6630260944366455\n",
" 132 7.606379e+00 4.892161e-02\n",
" * time: 0.6663720607757568\n",
" 133 7.606019e+00 5.897510e-02\n",
" * time: 0.669666051864624\n",
" 134 7.605895e+00 5.835775e-02\n",
" * time: 0.6737511157989502\n",
" 135 7.605529e+00 6.145676e-02\n",
" * time: 0.6781129837036133\n",
" 136 7.605441e+00 5.913657e-02\n",
" * time: 0.681225061416626\n",
" 137 7.604960e+00 6.140341e-02\n",
" * time: 0.6850600242614746\n",
" 138 7.604615e+00 7.197212e-02\n",
" * time: 0.6882419586181641\n",
" 139 7.604391e+00 6.654725e-02\n",
" * time: 0.6913149356842041\n",
" 140 7.604042e+00 4.288100e-02\n",
" * time: 0.6951639652252197\n",
" 141 7.603491e+00 4.574636e-02\n",
" * time: 0.6983311176300049\n",
" 142 7.603190e+00 3.852431e-02\n",
" * time: 0.7026081085205078\n",
" 143 7.602961e+00 4.645119e-02\n",
" * time: 0.7057540416717529\n",
" 144 7.602846e+00 4.211701e-02\n",
" * time: 0.7088649272918701\n",
" 145 7.602700e+00 4.313572e-02\n",
" * time: 0.7223649024963379\n",
" 146 7.602494e+00 4.806204e-02\n",
" * time: 0.7253549098968506\n",
" 147 7.602222e+00 2.716103e-02\n",
" * time: 0.7291650772094727\n",
" 148 7.602073e+00 3.925079e-02\n",
" * time: 0.732511043548584\n",
" 149 7.601807e+00 4.177805e-02\n",
" * time: 0.7370409965515137\n",
" 150 7.601649e+00 3.735440e-02\n",
" * time: 0.7407538890838623\n",
" 151 7.601484e+00 2.376040e-02\n",
" * time: 0.74434494972229\n",
" 152 7.601470e+00 4.903720e-02\n",
" * time: 0.7480709552764893\n",
" 153 7.601317e+00 3.932386e-02\n",
" * time: 0.7525091171264648\n",
" 154 7.601255e+00 4.931099e-02\n",
" * time: 0.7557470798492432\n",
" 155 7.601215e+00 4.414912e-02\n",
" * time: 0.7586669921875\n",
" 156 7.601134e+00 3.269668e-02\n",
" * time: 0.7621428966522217\n",
" 157 7.601022e+00 2.164684e-02\n",
" * time: 0.7657370567321777\n",
" 158 7.600899e+00 2.864477e-02\n",
" * time: 0.7692220211029053\n",
" 159 7.600712e+00 2.320747e-02\n",
" * time: 0.7735199928283691\n",
" 160 7.600634e+00 3.618709e-02\n",
" * time: 0.7770650386810303\n",
" 161 7.600579e+00 3.187546e-02\n",
" * time: 0.7806549072265625\n",
" 162 7.600535e+00 2.335649e-02\n",
" * time: 0.783958911895752\n",
" 163 7.600528e+00 4.300130e-02\n",
" * time: 0.7871699333190918\n",
" 164 7.600498e+00 2.436966e-02\n",
" * time: 0.790229082107544\n",
" 165 7.600399e+00 4.620966e-02\n",
" * time: 0.7935009002685547\n",
" 166 7.600281e+00 1.754702e-02\n",
" * time: 0.7974939346313477\n",
" 167 7.600153e+00 1.268561e-02\n",
" * time: 0.8015010356903076\n",
" 168 7.600101e+00 3.072953e-02\n",
" * time: 0.8048090934753418\n",
" 169 7.600038e+00 1.985024e-02\n",
" * time: 0.8092870712280273\n",
" 170 7.599987e+00 2.231722e-02\n",
" * time: 0.8130450248718262\n",
" 171 7.599944e+00 2.888140e-02\n",
" * time: 0.8163149356842041\n",
" 172 7.599870e+00 1.815027e-02\n",
" * time: 0.8202509880065918\n",
" 173 7.599850e+00 2.125707e-02\n",
" * time: 0.8235421180725098\n",
" 174 7.599782e+00 1.586047e-02\n",
" * time: 0.8278069496154785\n",
" 175 7.599747e+00 1.386194e-02\n",
" * time: 0.842379093170166\n",
" 176 7.599719e+00 1.542014e-02\n",
" * time: 0.8454849720001221\n",
" 177 7.599660e+00 1.137233e-02\n",
" * time: 0.8484539985656738\n",
" 178 7.599629e+00 1.981184e-02\n",
" * time: 0.8515310287475586\n",
" 179 7.599583e+00 1.536164e-02\n",
" * time: 0.8555169105529785\n",
" 180 7.599541e+00 1.844064e-02\n",
" * time: 0.8590860366821289\n",
" 181 7.599511e+00 1.749195e-02\n",
" * time: 0.863055944442749\n",
" 182 7.599475e+00 1.202908e-02\n",
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" 515 7.598695e+00 2.175180e-04\n",
" * time: 2.1524500846862793\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=1}",
"image/png": 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",
"text/html": [
"\n",
"\n"
],
"image/svg+xml": [
"\n",
"\n"
]
},
"metadata": {},
"execution_count": 5
}
],
"cell_type": "code",
"source": [
"terms = [Kinetic(),\n",
" ExternalFromReal(X -> pot(X...)),\n",
" PowerNonlinearity(C, α),\n",
" Magnetic(Apot),\n",
"]\n",
"model = Model(lattice; n_electrons=n_electrons,\n",
" terms=terms, spin_polarization=:spinless) # \"spinless electrons\"\n",
"basis = PlaneWaveBasis(model, Ecut, kgrid=(1, 1, 1))\n",
"scfres = direct_minimization(basis, tol=1e-5) # Reduce tol for production\n",
"heatmap(scfres.ρ.real[:, :, 1], c=:blues)"
],
"metadata": {},
"execution_count": 5
}
],
"nbformat_minor": 3,
"metadata": {
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.5.3"
},
"kernelspec": {
"name": "julia-1.5",
"display_name": "Julia 1.5.3",
"language": "julia"
}
},
"nbformat": 4
}