{
 "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     3.178874e+01     8.073477e+00\n",
      " * time: 0.0019261837005615234\n",
      "     1     2.979741e+01     5.177095e+00\n",
      " * time: 0.008530139923095703\n",
      "     2     2.136178e+01     5.751207e+00\n",
      " * time: 0.01683521270751953\n",
      "     3     1.751289e+01     7.333431e+00\n",
      " * time: 0.02464914321899414\n",
      "     4     1.192422e+01     2.676646e+00\n",
      " * time: 0.03176307678222656\n",
      "     5     9.798932e+00     1.021552e+00\n",
      " * time: 0.03886914253234863\n",
      "     6     9.152591e+00     1.245030e+00\n",
      " * time: 0.04542708396911621\n",
      "     7     8.787339e+00     7.303126e-01\n",
      " * time: 0.05136704444885254\n",
      "     8     8.488029e+00     5.894573e-01\n",
      " * time: 0.05793118476867676\n",
      "     9     8.298257e+00     5.768405e-01\n",
      " * time: 0.063751220703125\n",
      "    10     8.145146e+00     5.158911e-01\n",
      " * time: 0.0696101188659668\n",
      "    11     8.033811e+00     4.742253e-01\n",
      " * time: 0.0761561393737793\n",
      "    12     7.951600e+00     4.700619e-01\n",
      " * time: 0.11073899269104004\n",
      "    13     7.923141e+00     6.973155e-01\n",
      " * time: 0.11396503448486328\n",
      "    14     7.870060e+00     4.118104e-01\n",
      " * time: 0.11706900596618652\n",
      "    15     7.857083e+00     5.350892e-01\n",
      " * time: 0.12032914161682129\n",
      "    16     7.820183e+00     4.187180e-01\n",
      " * time: 0.12432599067687988\n",
      "    17     7.781929e+00     5.020283e-01\n",
      " * time: 0.12743902206420898\n",
      "    18     7.755426e+00     4.000637e-01\n",
      " * time: 0.13132405281066895\n",
      "    19     7.741935e+00     4.450722e-01\n",
      " * time: 0.13444304466247559\n",
      "    20     7.733792e+00     3.611611e-01\n",
      " * time: 0.1376180648803711\n",
      "    21     7.722208e+00     2.701878e-01\n",
      " * time: 0.1407790184020996\n",
      "    22     7.713792e+00     3.308856e-01\n",
      " * time: 0.1438741683959961\n",
      "    23     7.707877e+00     3.095860e-01\n",
      " * time: 0.147003173828125\n",
      "    24     7.702640e+00     2.850163e-01\n",
      " * time: 0.15026307106018066\n",
      "    25     7.693755e+00     2.520440e-01\n",
      " * time: 0.15374016761779785\n",
      "    26     7.686768e+00     2.699542e-01\n",
      " * time: 0.15687012672424316\n",
      "    27     7.685180e+00     2.624248e-01\n",
      " * time: 0.16009020805358887\n",
      "    28     7.681179e+00     1.951314e-01\n",
      " * time: 0.16480302810668945\n",
      "    29     7.677673e+00     2.632465e-01\n",
      " * time: 0.1702280044555664\n",
      "    30     7.672823e+00     2.599632e-01\n",
      " * time: 0.1748790740966797\n",
      "    31     7.664361e+00     1.334921e-01\n",
      " * time: 0.18097305297851562\n",
      "    32     7.662072e+00     2.750370e-01\n",
      " * time: 0.18641018867492676\n",
      "    33     7.656434e+00     1.760239e-01\n",
      " * time: 0.1929171085357666\n",
      "    34     7.656242e+00     2.819530e-01\n",
      " * time: 0.19822907447814941\n",
      "    35     7.651541e+00     1.863965e-01\n",
      " * time: 0.20467400550842285\n",
      "    36     7.648331e+00     2.164933e-01\n",
      " * time: 0.20975208282470703\n",
      "    37     7.647984e+00     2.305950e-01\n",
      " * time: 0.21582913398742676\n",
      "    38     7.644223e+00     1.377365e-01\n",
      " * time: 0.22176098823547363\n",
      "    39     7.640991e+00     1.308886e-01\n",
      " * time: 0.2278749942779541\n",
      "    40     7.638552e+00     1.094372e-01\n",
      " * time: 0.25028109550476074\n",
      "    41     7.637247e+00     1.559888e-01\n",
      " * time: 0.2533860206604004\n",
      "    42     7.634933e+00     1.335024e-01\n",
      " * time: 0.2563471794128418\n",
      "    43     7.633332e+00     1.378269e-01\n",
      " * time: 0.2592802047729492\n",
      "    44     7.631486e+00     1.471017e-01\n",
      " * time: 0.262559175491333\n",
      "    45     7.629342e+00     7.429038e-02\n",
      " * time: 0.26625514030456543\n",
      "    46     7.627941e+00     7.927926e-02\n",
      " * time: 0.26926112174987793\n",
      "    47     7.627447e+00     1.294184e-01\n",
      " * time: 0.2722771167755127\n",
      "    48     7.625968e+00     7.551238e-02\n",
      " * time: 0.2768821716308594\n",
      "    49     7.625001e+00     6.862656e-02\n",
      " * time: 0.27999305725097656\n",
      "    50     7.624053e+00     6.496034e-02\n",
      " * time: 0.2830522060394287\n",
      "    51     7.623417e+00     6.819647e-02\n",
      " * time: 0.2860841751098633\n",
      "    52     7.622818e+00     4.990528e-02\n",
      " * time: 0.28994321823120117\n",
      "    53     7.622578e+00     6.896675e-02\n",
      " * time: 0.2931480407714844\n",
      "    54     7.622075e+00     3.735801e-02\n",
      " * time: 0.2970302104949951\n",
      "    55     7.621869e+00     6.357034e-02\n",
      " * time: 0.30001115798950195\n",
      "    56     7.621503e+00     4.867156e-02\n",
      " * time: 0.3030731678009033\n",
      "    57     7.621233e+00     5.502045e-02\n",
      " * time: 0.30612802505493164\n",
      "    58     7.620985e+00     4.253322e-02\n",
      " * time: 0.3092520236968994\n",
      "    59     7.620853e+00     5.839866e-02\n",
      " * time: 0.31233716011047363\n",
      "    60     7.620371e+00     5.027390e-02\n",
      " * time: 0.31530308723449707\n",
      "    61     7.620139e+00     6.203246e-02\n",
      " * time: 0.31838321685791016\n",
      "    62     7.619735e+00     5.082239e-02\n",
      " * time: 0.3214151859283447\n",
      "    63     7.619393e+00     4.064180e-02\n",
      " * time: 0.3247561454772949\n",
      "    64     7.619333e+00     6.924952e-02\n",
      " * time: 0.32776904106140137\n",
      "    65     7.619021e+00     4.010354e-02\n",
      " * time: 0.3307371139526367\n",
      "    66     7.618750e+00     7.635480e-02\n",
      " * time: 0.3337230682373047\n",
      "    67     7.618612e+00     4.561417e-02\n",
      " * time: 0.33678722381591797\n",
      "    68     7.618541e+00     7.632950e-02\n",
      " * time: 0.3405771255493164\n",
      "    69     7.618310e+00     7.969570e-02\n",
      " * time: 0.34369611740112305\n",
      "    70     7.617821e+00     4.287992e-02\n",
      " * time: 0.3630940914154053\n",
      "    71     7.617425e+00     6.870406e-02\n",
      " * time: 0.3660430908203125\n",
      "    72     7.616875e+00     3.366292e-02\n",
      " * time: 0.3699030876159668\n",
      "    73     7.616566e+00     5.532085e-02\n",
      " * time: 0.372866153717041\n",
      "    74     7.616297e+00     3.974816e-02\n",
      " * time: 0.3768000602722168\n",
      "    75     7.616243e+00     5.849349e-02\n",
      " * time: 0.37979817390441895\n",
      "    76     7.616223e+00     4.705534e-02\n",
      " * time: 0.3827931880950928\n",
      "    77     7.616054e+00     6.111076e-02\n",
      " * time: 0.3867170810699463\n",
      "    78     7.615660e+00     4.233811e-02\n",
      " * time: 0.39074206352233887\n",
      "    79     7.615379e+00     7.147692e-02\n",
      " * time: 0.3938741683959961\n",
      "    80     7.614933e+00     6.416441e-02\n",
      " * time: 0.3968780040740967\n",
      "    81     7.614879e+00     4.140046e-02\n",
      " * time: 0.39997005462646484\n",
      "    82     7.614550e+00     3.417496e-02\n",
      " * time: 0.4038112163543701\n",
      "    83     7.614260e+00     2.930962e-02\n",
      " * time: 0.40680503845214844\n",
      "    84     7.614059e+00     6.696491e-02\n",
      " * time: 0.4098021984100342\n",
      "    85     7.613832e+00     4.517744e-02\n",
      " * time: 0.41358208656311035\n",
      "    86     7.613485e+00     3.696788e-02\n",
      " * time: 0.4175751209259033\n",
      "    87     7.613430e+00     4.164094e-02\n",
      " * time: 0.4206051826477051\n",
      "    88     7.613236e+00     2.950946e-02\n",
      " * time: 0.4236412048339844\n",
      "    89     7.613060e+00     4.014367e-02\n",
      " * time: 0.42660999298095703\n",
      "    90     7.612920e+00     4.530450e-02\n",
      " * time: 0.4296431541442871\n",
      "    91     7.612666e+00     4.512535e-02\n",
      " * time: 0.4337332248687744\n",
      "    92     7.612589e+00     4.888226e-02\n",
      " * time: 0.43712615966796875\n",
      "    93     7.612517e+00     5.051830e-02\n",
      " * time: 0.4408760070800781\n",
      "    94     7.612259e+00     4.780878e-02\n",
      " * time: 0.4441821575164795\n",
      "    95     7.612153e+00     4.427455e-02\n",
      " * time: 0.4472529888153076\n",
      "    96     7.612051e+00     5.523071e-02\n",
      " * time: 0.4503471851348877\n",
      "    97     7.611797e+00     4.794785e-02\n",
      " * time: 0.45337820053100586\n",
      "    98     7.611531e+00     4.616947e-02\n",
      " * time: 0.4676392078399658\n",
      "    99     7.611316e+00     3.163070e-02\n",
      " * time: 0.4714641571044922\n",
      "   100     7.611276e+00     4.972612e-02\n",
      " * time: 0.47460412979125977\n",
      "   101     7.611120e+00     4.902382e-02\n",
      " * time: 0.4784560203552246\n",
      "   102     7.610873e+00     4.003331e-02\n",
      " * time: 0.48153209686279297\n",
      "   103     7.610599e+00     2.962464e-02\n",
      " * time: 0.485288143157959\n",
      "   104     7.610364e+00     2.879457e-02\n",
      " * time: 0.48934412002563477\n",
      "   105     7.610209e+00     2.745396e-02\n",
      " * time: 0.49321413040161133\n",
      "   106     7.610100e+00     3.967563e-02\n",
      " * time: 0.4966590404510498\n",
      "   107     7.609961e+00     3.071004e-02\n",
      " * time: 0.5007731914520264\n",
      "   108     7.609774e+00     2.141246e-02\n",
      " * time: 0.5046210289001465\n",
      "   109     7.609687e+00     1.699303e-02\n",
      " * time: 0.5085041522979736\n",
      "   110     7.609656e+00     3.522981e-02\n",
      " * time: 0.5128481388092041\n",
      "   111     7.609654e+00     3.987945e-02\n",
      " * time: 0.5158631801605225\n",
      "   112     7.609501e+00     2.501769e-02\n",
      " * time: 0.519017219543457\n",
      "   113     7.609378e+00     3.072030e-02\n",
      " * time: 0.5220541954040527\n",
      "   114     7.609239e+00     3.377606e-02\n",
      " * time: 0.5250520706176758\n",
      "   115     7.609011e+00     2.629497e-02\n",
      " * time: 0.5283660888671875\n",
      "   116     7.608991e+00     4.683545e-02\n",
      " * time: 0.5314991474151611\n",
      "   117     7.608933e+00     3.356111e-02\n",
      " * time: 0.5345752239227295\n",
      "   118     7.608736e+00     2.505826e-02\n",
      " * time: 0.5377521514892578\n",
      "   119     7.608555e+00     3.665424e-02\n",
      " * time: 0.5407431125640869\n",
      "   120     7.608372e+00     2.363868e-02\n",
      " * time: 0.5449399948120117\n",
      "   121     7.608194e+00     2.957404e-02\n",
      " * time: 0.5493760108947754\n",
      "   122     7.608047e+00     1.836890e-02\n",
      " * time: 0.5532190799713135\n",
      "   123     7.607988e+00     2.857453e-02\n",
      " * time: 0.556779146194458\n",
      "   124     7.607896e+00     2.995345e-02\n",
      " * time: 0.5611422061920166\n",
      "   125     7.607725e+00     1.992903e-02\n",
      " * time: 0.5763092041015625\n",
      "   126     7.607663e+00     2.746698e-02\n",
      " * time: 0.5792632102966309\n",
      "   127     7.607529e+00     2.106534e-02\n",
      " * time: 0.5830950736999512\n",
      "   128     7.607421e+00     2.387112e-02\n",
      " * time: 0.5860772132873535\n",
      "   129     7.607341e+00     2.323160e-02\n",
      " * time: 0.5892210006713867\n",
      "   130     7.607216e+00     3.027004e-02\n",
      " * time: 0.5922009944915771\n",
      "   131     7.607112e+00     2.959508e-02\n",
      " * time: 0.5951700210571289\n",
      "   132     7.607094e+00     2.932824e-02\n",
      " * time: 0.5982379913330078\n",
      "   133     7.607015e+00     2.870490e-02\n",
      " * time: 0.6014730930328369\n",
      "   134     7.606992e+00     3.914016e-02\n",
      " * time: 0.6047031879425049\n",
      "   135     7.606850e+00     2.764842e-02\n",
      " * time: 0.6077940464019775\n",
      "   136     7.606713e+00     3.164189e-02\n",
      " * time: 0.61080002784729\n",
      "   137     7.606542e+00     2.572833e-02\n",
      " * time: 0.6146290302276611\n",
      "   138     7.606435e+00     1.820954e-02\n",
      " * time: 0.6183362007141113\n",
      "   139     7.606255e+00     2.055410e-02\n",
      " * time: 0.6223130226135254\n",
      "   140     7.606119e+00     1.972259e-02\n",
      " * time: 0.6263031959533691\n",
      "   141     7.606002e+00     2.063439e-02\n",
      " * time: 0.6293540000915527\n",
      "   142     7.605994e+00     2.788884e-02\n",
      " * time: 0.6323561668395996\n",
      "   143     7.605975e+00     3.637467e-02\n",
      " * time: 0.6356191635131836\n",
      "   144     7.605871e+00     2.875584e-02\n",
      " * time: 0.6395890712738037\n",
      "   145     7.605787e+00     3.737618e-02\n",
      " * time: 0.6427321434020996\n",
      "   146     7.605721e+00     4.622652e-02\n",
      " * time: 0.6458430290222168\n",
      "   147     7.605668e+00     3.754051e-02\n",
      " * time: 0.649224042892456\n",
      "   148     7.605544e+00     3.361410e-02\n",
      " * time: 0.6524381637573242\n",
      "   149     7.605355e+00     2.880915e-02\n",
      " * time: 0.656400203704834\n",
      "   150     7.605282e+00     3.323432e-02\n",
      " * time: 0.6595320701599121\n",
      "   151     7.605104e+00     3.567696e-02\n",
      " * time: 0.6632671356201172\n",
      "   152     7.605087e+00     4.277122e-02\n",
      " * time: 0.6663320064544678\n",
      "   153     7.604903e+00     3.671312e-02\n",
      " * time: 0.6702370643615723\n",
      "   154     7.604721e+00     3.423207e-02\n",
      " * time: 0.6845030784606934\n",
      "   155     7.604599e+00     3.365080e-02\n",
      " * time: 0.6875340938568115\n",
      "   156     7.604468e+00     2.139750e-02\n",
      " * time: 0.690709114074707\n",
      "   157     7.604294e+00     2.916278e-02\n",
      " * time: 0.6946451663970947\n",
      "   158     7.604144e+00     1.680242e-02\n",
      " * time: 0.698479175567627\n",
      "   159     7.604071e+00     4.157167e-02\n",
      " * time: 0.7015590667724609\n",
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      "   628     7.592300e+00     1.921035e-04\n",
      " * time: 2.515496015548706\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=1}",
      "image/png": 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      ]
     },
     "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
  }
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