{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Bond approximation\n", "\n", "In this notebook I'll have a look at how exactly the bond approximation works. Starting point is the fixed charge system, with two electrons per cell and therefore 28 states per cell. We can represent these 28 states in a different basis, the bond basis: Two electrons make up a bond and there are six bonds, four on the edges of the cell and two on the diagonal. Each bond consists of three triplet and and singlet state. Together with the four double occupied states, this gives the 28 states ($6 \\cdot4 + 4 = 28$).\n", "\n", "Now we neglect all doubly occupied states and the spin, reducing the four states for every bond to only one, yielding six states (the six bonds) per cell in total. In what limits is this approximation valid and how does it actually work?\n", "\n", "One obvious requirement is that $T \\ll U$ (in my code I usually use $V0 = V_0 = U$), the doubly occupied states need to be gapped out.\n", "\n", "By representing each bond by only one state we assume that the triplet and singlet states are equivalent and energetically degenerate. This is not correct. In a simplified picture we would expect that virtual excitations to higher energy states yield a lower enegy for the singlet state, similar in fashion to how the Heisenberg model can be derived as the low energy limit of the Hubbard model (where we have $J \\sim \\frac{t^2}{U}$).\n", "\n", "We plot the (low) energy histogram of both the fixed charge and the bond model for a single active QCA cell (there's still the static driving cell) and suitably chosen parameters." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# increases the resolution of the pngs displayed inline, \n", "# so they are big enough even for a small figsize\n", "# I should also be able to set this in ipython_notebook_config.py \n", "# in the profile directory\n", "%matplotlib inline\n", "c = %config InlineBackend.rc\n", "c['savefig.dpi'] = 150\n", "%config InlineBackend.figure_format='png'\n", "%config InlineBackend.rc = c\n", "%matplotlib inline\n", "\n", "# imports\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "import numpy as np\n", "import qca\n", "print(qca.__version__)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "8.2.0\n" ] } ], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "grey = '#666666'\n", "lw = 0.5\n", "margin = 0.15\n", "mpl.rcParams['figure.figsize'] = (5,5)\n", "mpl.rcParams['font.size'] = 9\n", "mpl.rcParams['font.sans-serif'].insert(0,'Open Sans')\n", "mpl.rcParams['legend.fontsize'] = 'medium'\n", "mpl.rcParams['lines.linewidth'] = lw\n", "mpl.rcParams['patch.linewidth'] = lw\n", "mpl.rcParams['axes.linewidth'] = lw\n", "mpl.rcParams['patch.edgecolor'] = grey\n", "mpl.rcParams['axes.edgecolor'] = grey\n", "mpl.rcParams['axes.labelcolor'] = grey\n", "mpl.rcParams['text.color'] = grey\n", "mpl.rcParams['xtick.color'] = grey\n", "mpl.rcParams['ytick.color'] = grey\n", "mpl.rcParams['xtick.major.size'] = 3\n", "mpl.rcParams['xtick.minor.size'] = 1\n", "mpl.rcParams['xtick.major.width'] = 0.3\n", "mpl.rcParams['xtick.minor.width'] = 0.3\n", "mpl.rcParams['ytick.major.size'] = 3\n", "mpl.rcParams['ytick.minor.size'] = 1\n", "mpl.rcParams['ytick.major.width'] = 0.3\n", "mpl.rcParams['ytick.minor.width'] = 0.3\n", "mpl.rcParams['figure.subplot.left'] = margin\n", "mpl.rcParams['figure.subplot.right'] = 1-margin\n", "mpl.rcParams['figure.subplot.bottom'] = margin\n", "mpl.rcParams['figure.subplot.top'] = 1-margin\n", "mpl.rcParams['figure.subplot.wspace'] = 2*margin\n", "mpl.rcParams['figure.subplot.hspace'] = 2*margin" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [ "s_f = qca.QcaFixedCharge()\n", "s_b = qca.QcaBond()\n", "\n", "# Wire geometry\n", "N = 1\n", "V1 = 30.0\n", "boa = 2\n", "P_0 = 1\n", "\n", "# Other parameters\n", "T = 1E-6\n", "beta = 1/T\n", "V0 = 1E6\n", "\n", "# Set the systems up\n", "s_f.l = qca.Wire(N,V1,boa,P_0)\n", "s_b.l = qca.Wire(N,V1,boa,P_0)\n", "s_f.V0 = V0\n", "s_b.V0 = V0\n", "s_f.beta = beta\n", "s_b.beta = beta\n", "\n", "s_f.init()\n", "s_f.run()\n", "s_b.init()\n", "s_b.run()\n", "\n", "Es_b = np.array(s_b.energies())\n", "Es_b.sort()\n", "Es_f = np.array(s_f.energies())\n", "Es_f.sort()\n", "Emin = np.concatenate((Es_b, Es_f)).min()\n", "Es_b -= Emin\n", "Es_f -= Emin\n", "Emax = np.concatenate((Es_b, Es_f)).max()\n", "Emin = 0\n", "Emax = 10\n", "bins = np.arange(Emin,Emax,1E-4)\n", "h_f,_ = np.histogram(Es_f,bins)\n", "h_b,_ = np.histogram(Es_b,bins)\n", "\n", "bins = bins[:-1]\n", "\n", "fig = plt.figure(figsize=(2.5,2.5))\n", "#fig = plt.figure(figsize=(5,5))\n", "p = fig.add_subplot(1,1,1)\n", "p.plot(bins,h_f, label='Fixed')\n", "p.plot(bins,-h_b, label='Bond')\n", "p.set_xlim((-1,10))\n", "p.set_ylim((-1,3))\n", "p.set_xlabel('energy')\n", "p.set_ylabel('state count')\n", "p.get_yaxis().set_ticklabels([1,'',0,'',1,'',2,'',3])\n", "p.legend()\n", "\n", "fig.savefig('../plots/chapter02/bond_approximation1.pdf')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Pf4SLi0uzfz8hIcHifK5Go4FGoxG6VAAc3mUL3C/UHBkZGcjIyDCb1ng7sVhkGbQ6nQ4b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\n", "text": [ "" ] } ], "prompt_number": 32 }, { "cell_type": "markdown", "metadata": {}, "source": [ "From this plot we see that for each single bond state we have three corresponding fixed charge states---the triplet---and one close by singlet state (hence four corresponding fixed charge states in total). We investigate how the singlet-triplet splitting depends on various parameters, like $U$, $V_1 = \\frac{1}{a}$, and $\\frac{b}{a}$. To do that we pick out the two lowest lying singlet-triplet pairs in the plot above as a sample. Hence our investigation is not thorough. Still, it should allow us to get an idea of how the system works." ] }, { "cell_type": "code", "collapsed": false, "input": [ "s_f = qca.QcaFixedCharge()\n", "\n", "def computeDeltaE(V0,V1,boa,P_0):\n", " # Wire geometry\n", " N = 1\n", " # Other parameters\n", " T = 1E-6\n", " beta = 1/T\n", " #V0 = 1E6\n", " # Set the systems up\n", " s_f.l = qca.Wire(N,V1,boa,P_0)\n", " s_f.V0 = V0\n", " s_f.beta = beta\n", " s_f.init()\n", " s_f.run()\n", " # Energies\n", " Es_f = np.array(s_f.energies())\n", " Es_f.sort()\n", " Emin = Es_f.min()\n", " Es_f -= Emin\n", " return (Es_f[1]-Es_f[0],Es_f[7]-Es_f[6])\n", "\n", "deltaE1 = []\n", "for V1 in np.linspace(20,200,100):\n", " E1,E2 = computeDeltaE(1E6,V1,100,1.0)\n", " deltaE1.append([V1,E1,E2])\n", "deltaE1 = np.array(deltaE1)\n", "\n", "deltaE2 = []\n", "for V1 in np.linspace(20,200,100):\n", " E1,E2 = computeDeltaE(1E6,V1,2,1.0)\n", " deltaE2.append([V1,E1,E2])\n", "deltaE2 = np.array(deltaE2)\n", "\n", "deltaE3 = []\n", "for V0 in np.linspace(200,2000,100):\n", " E1,E2 = computeDeltaE(V0,100.0,2,1.0)\n", " deltaE3.append([V0,E1,E2])\n", "deltaE3 = np.array(deltaE3)\n", "\n", "deltaE4 = []\n", "for ba in np.linspace(2,20,100):\n", " E1,E2 = computeDeltaE(1E6,100.0,ba,1.0)\n", " deltaE4.append([ba,E1,E2])\n", "deltaE4 = np.array(deltaE4)\n", "\n", "deltaE5 = []\n", "for V1 in np.linspace(20,200,100):\n", " E1,E2 = computeDeltaE(1E6,V1,100,0)\n", " deltaE5.append([V1,E1,E2])\n", "deltaE5 = np.array(deltaE5)\n", "\n", "deltaE6 = []\n", "for V1 in np.linspace(20,200,100):\n", " E1,E2 = computeDeltaE(1E6,V1,2,0)\n", " deltaE6.append([V1,E1,E2])\n", "deltaE6 = np.array(deltaE6)\n", "\n", "deltaE7 = []\n", "for V0 in np.linspace(200,2000,100):\n", " E1,E2 = computeDeltaE(V0,100.0,2,0)\n", " deltaE7.append([V0,E1,E2])\n", "deltaE7 = np.array(deltaE7)\n", "\n", "deltaE8 = []\n", "for ba in np.linspace(2,20,100):\n", " E1,E2 = computeDeltaE(1E6,100.0,ba,0)\n", " deltaE8.append([ba,E1,E2])\n", "deltaE8 = np.array(deltaE8)\n", "\n", "# Plotting\n", "fig = plt.figure(figsize=(20,10))\n", "\n", "f1 = np.vectorize(lambda x: 10 / x**1)\n", "fs1 = f1(deltaE1[:,0])\n", "p = fig.add_subplot(2,4,1)\n", "p.plot(deltaE1[:,0],deltaE1[:,1],label='$\\Delta E_1$')\n", "p.plot(deltaE1[:,0],deltaE1[:,2],label='$\\Delta E_2$')\n", "p.plot(deltaE1[:,0],fs1,label='$f(V_1)=a V_1^{-1}$')\n", "p.set_xscale('log')\n", "p.set_yscale('log')\n", "p.set_xlabel('$V_1$')\n", "p.set_ylabel('energy')\n", "p.set_title('$P_0 = 1$, $b/a = 100$')\n", "p.legend()\n", "\n", "f2 = np.vectorize(lambda x: 15000 / x**3)\n", "fs2 = f2(deltaE2[:,0])\n", "p = fig.add_subplot(2,4,2)\n", "p.plot(deltaE2[:,0],deltaE2[:,1])\n", "p.plot(deltaE2[:,0],deltaE2[:,2])\n", "p.plot(deltaE2[:,0],fs2,label='$f(V_1)=a V_1^{-3}$')\n", "p.set_xscale('log')\n", "p.set_yscale('log')\n", "p.set_xlabel('$V_1$')\n", "#p.set_ylabel('energy')\n", "p.set_title('$P_0 = 1$, $b/a = 2$')\n", "p.legend()\n", "\n", "p = fig.add_subplot(2,4,3)\n", "p.plot(deltaE3[:,0],deltaE3[:,1])\n", "p.plot(deltaE3[:,0],deltaE3[:,2])\n", "p.set_xlabel('$U$')\n", "#p.set_ylabel('energy')\n", "p.set_title('$P_0 = 1$, $b/a = 2$, $V_1 = 100$')\n", "\n", "p = fig.add_subplot(2,4,4)\n", "p.plot(deltaE4[:,0],deltaE4[:,1])\n", "p.plot(deltaE4[:,0],deltaE4[:,2])\n", "p.set_xlabel('$b/a$')\n", "#p.set_ylabel('energy')\n", "p.set_title('$P_0 = 1$, $V_1 = 100$')\n", "\n", "p = fig.add_subplot(2,4,5)\n", "p.plot(deltaE5[:,0],deltaE5[:,1])\n", "p.plot(deltaE5[:,0],deltaE5[:,2])\n", "p.plot(deltaE5[:,0],fs1,label='$f(V_1)=a V_1^{-1}$')\n", "p.set_xscale('log')\n", "p.set_yscale('log')\n", "p.set_xlabel('$V_1$')\n", "p.set_ylabel('energy')\n", "p.set_title('$P_0 = 0$, $b/a = 100$')\n", "p.legend()\n", "\n", "p = fig.add_subplot(2,4,6)\n", "p.plot(deltaE6[:,0],deltaE6[:,1])\n", "p.plot(deltaE6[:,0],deltaE6[:,2])\n", "p.plot(deltaE6[:,0],fs1,label='$f(V_1)=a V_1^{-1}$')\n", "p.set_xscale('log')\n", "p.set_yscale('log')\n", "p.set_xlabel('$V_1$')\n", "#p.set_ylabel('energy')\n", "p.set_title('$P_0 = 0$, $b/a = 2$')\n", "p.legend()\n", "\n", "p = fig.add_subplot(2,4,7)\n", "p.plot(deltaE7[:,0],deltaE7[:,1])\n", "p.plot(deltaE7[:,0],deltaE7[:,2])\n", "p.set_xlabel('$U$')\n", "#p.set_ylabel('energy')\n", "p.set_title('$P_0 = 0$, $b/a = 2$, $V_1 = 100$')\n", "\n", "p = fig.add_subplot(2,4,8)\n", "p.plot(deltaE8[:,0],deltaE8[:,1])\n", "p.plot(deltaE8[:,0],deltaE8[:,2])\n", "p.set_xlabel('$b/a$')\n", "p.set_title('$P_0 = 0$, $V_1 = 100$')\n", "#p.set_ylabel('energy')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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x40b9/Oc/r7Of1WrVVVddpUWLFmn58uW65ZZbqu3PzMyUwWAIKDTx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v6qbX5aOfPgpD4pIk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k+GpUuhR48cd2OLj4dXX4XGjaF6dfj00/3H/Kv6v+hSqQv10uu59Z8kSZIk6W+xerWFJpKk\n6GShiRRtTjkFMjKgTx9IS4toqBNPhLlzYtg4dBBrVx1P81HN2bZzW0RjSpKkKFGsGMyYERz335/j\n6UKhoKlbr15BZ5MFC/Yf07tWbxqf3pikIUms+31djmNKkiRJkvRXLDSRJEUrC02kaHTGGTBtGtx6\nK4wbF9FQZcrA3NlxbBo8gq+/CtF2bFt27NoR0ZiSJClKlCwZFMgOHgxPPhmWKbt3h+eeg4YNYcqU\nfc+FQiGeSH6C6idXJ2WoW/9JkiRJkiJr9WooWza3s5AkKfwsNJGiVZUqMGECXHllcAMngk49Fd6Y\nncCmV8bx4efr6DqhK7t274poTEmSFCXKlAm2/uvXD155JSxTtm4Nr70GqamQnr7vuVAoxPONnuf0\n40536z9JkiRJUkStWmVHE0lSdLLQRIpmNWrAyJHQpg3Mnx/RUOXLwxsZBdj88iTmfbqCG6bcQGZm\nZkRjSpKkKFGhQrCFzu23w5gxYZmyXr2gfuW226B//33PxcbEMrjZYI4rcBwtRrVw6z9JkiRJUthl\nZrp1jiQpelloIkW7+vVh4EBo0gSWLo1oqAoVYO70ImwZOJ0pHy7gXzP/ZbGJJEnKmvPOg8mT4dpr\ngy0Aw6BKFZg3L9hK5/bbgx/59oiLiWNky5Fkkkm7se3YuXtnWGJKkiRJkgSwbh3s2gUlSuR2JpIk\nhZ+FJtLRoFUrePxxSEmBzz+PaKgzz4TZk4uzdWAGwz+YzANvPhDReJIkKYpUrRp0NGnfHt5+OyxT\n/uMf8M47MH16sKPgzj/UkyTEJfB6m9dZu2Ut3SZ0Y3fm7rDElCRJkiRpTzeTGO/ESZKikP+8SUeL\nbt2CR3kTE4MVbgSdey5kjD+BrS/P4rl3BvPE/CciGk+SJEWRevVg0CBo1gz++9+wTFm6NLz5ZlBv\n26oV/P773nMF4gswuf1kPl37KTdOudFubJIkSZKksFi1ym1zJEnRy0IT6Whyyy1BwUliIqxZE9FQ\nlSvDzDFl2PHKbB6d+29e+uCliMaTJElRpFkzGDAAGjaETz8Ny5TFisGMGUHb4pQUWL9+77kiCUWY\n0XEG81bP47aM2yw2kSRJkiTl2J6OJpIkRSMLTaSjzX33BTdt6teH336LaKiLLoKpQ09j56AMbp9x\nL0M/HBrReJIkKYqkpgbrlqQk+PrrsExZoACMGwennAJ16uxbd1s8f3EyUjOY8NkEHnrrobDEkyRJ\nkiQdvSw0kSRFs7jcTkDS3ywUgv794aqroFEjmDkTChaMWLjq1WHSq2dx+TXTuIFkCsYXpPmZzSMW\nT5IkRZEbbwxajyQmwttvB3vg5FB8PAweDLfeCjVqQEZGUHgCUKpQKWZ1msVlgy6j8DGF6VGtR47j\nSVJu+OSTTxg/fjw//PADRYoUoXbt2iQlJWXp2lWrVvHoo4/y8MMPU7x48X3OzZ8/n4yMDH7++WeK\nFy9O7dq1qVu37j5jvvjiC8aPH8+qVatISEjgggsuoGnTpuTLly9s30+SJEWHaF+zrFoFtWqFbTpJ\nko4odjSRjkYxMfDyy3DiidCiBWzbFtFwNWvCuGcvgBET6DzuSmasnBHReJIkKYrceSe0bAnJybBu\nXVimjImBf/87aJpSo8a+u/OULVqWWamzeHz+47z835fDEk+S/k5ffvklzz77LKX/j707D4+yvPc/\n/p4shACBiKwuKChlUTBEUUFkTYDIjsimgLgVFFqRolbr0lOsFdda3LAuICKKyE6Q5IeiqKVWDMWD\nSpVWlFoQlYAsCST8/pgjPRxiRZknk8y8X9fFRXlm5vl880fxZuYz992wIWPHjuXss89m7ty5LFu2\n7Htfu3nzZqZOnVrmEWKrVq1ixowZtG7dmvHjx9OuXTvmzJlDbm7uwed89tln3H///aSmpjJmzBgG\nDBjAX/7yFx57zKNUJUnSoeJhzeKOJpKkWOaOJlK8SkyEmTOhXz8YPhyefx6SgvsrISsLZk/pwJCb\nnucihrDkkgWcf9L5geVJkqQYEQrB734XPvIvJwfy8yEtLSK3veUWqF07/A2z3Fw488zwY02PbUre\niDy6TO9C9SrVGd5q+FHnSVJ5WbRoEY0aNWL06NEAtGzZkpKSEnJzc+nWrRvJycmHvaakpIQVK1aw\naNEikr7j34W5ublkZmYyYEB4h8pmzZqxZcsWXnnlFXJycgDIz8+nRo0a/PSnPyUxMfHga6dPn86W\nLVuoX79+pH9cSZJUScXDmsWiiSQplrmjiRTPUlJg7lzYsiV8lE5paaBxF1wAz9yeTem8p+j9bH/e\n3vx2oHmSJClGhELw8MPQpEm4JLt3b8Rufc014d1NuneHlSv/ff30eqezdPhSxi0dx4IPFkQsT5KC\ntG/fPjZs2ECbNm0OuZ6ZmUlRUREfffRRma9bt24dixcvJicnh4EDB5b5nPHjx3PhhRceci0xMZH9\n+/cf/HP//v0ZP378IR/YfPu///fzJElSfIuHNUtJCWzebNFEkhS7LJpI8a56dVi8GNauhQkToIzt\nBiOpf394YlI/Shb9ge4zLuC9re8FmidJkmJEYiLMmAHVqsGQIbBvX8RuffHF8PTTMGBAeFn0rbbH\nt2X+0PmMXjCavI/zIpYnSUHZtm0bJSUlh30Lt27dugBs2bKlzNedfPLJ3HnnneTk5JCQUPZbRQ0a\nNODYY48FYNeuXaxatYrVq1fTqVOng89JT0/n+OOPB6CoqIj333+f+fPnc8oppxy8LkmSFA9rln/9\nC1JToVatiNxOkqQKx6NzJEF6Orz8MnTsCLffDr/+daBxQ4ZAcfFwrn7iG7omdOfNK1/j1NqnBpop\nSZJiQHIyzJkTPkJn9Ohw8eQ73lz8ofr0gZdeggsvhD/8IXyyIEDHkzry3IXPMeTFISwatojzGp0X\nkTxJCsKePXsAqFq16iHXv/3z3u/YESo9Pf2IMz7++GPuvvtuAE466SSysrIOe86BAweYOHEi+/fv\np3r16gwdOvSI7y9JkmJfPKxZvj02JxSK2C0lSapQ3NFEUli9epCXB9Onw333BR43YgTcd/FV7Pl/\nv6DTE1l8Wvhp4JmSJCkGpKbCwoWwYQOMGxfR3dg6d4Zly+Daa+Gxx/59vcepPXii7xP0nd2XNZ+v\niVieJEXage/5OzEUgU866tSpw8SJExk1ahSFhYVMmTKF4uLiQ55TWlrKNddcw9VXX039+vW55557\n+Oyzz446W5IkxYZ4WLN8WzSRJClWuaOJpH878cRw2aRjx/CefpdfHmjclVdCUdF1/HL5DjomduNP\nV71O/Rr1v/+FkiQpvtWsCbm54TXLzTfDb38bsVu3bQuvvALZ2VBYCNdfH74+oMUAvin+hp4ze/Lq\npa/Ssm7LiGVKUqSkpqYCh38L+Ns/f/v40ahVqxa1atWiadOm1KlTh3vvvZc1a9Zw7rnnHnxOYmIi\nLVq0AKBp06bcdNNNrFixgpEjR37v/adPn37YVvgZGRlkZGQc9eySJP1QBQUFFBQUHHKttLQ0StPE\njnhYs2zaZNFEklR+orFmsWgi6VBNm4aP0enaFdLSYPDgQOPGjYPdu29j8ls76ZyUzRtXvkrt1NqB\nZkqSpBhw7LHhgmyHDuGC7A03ROzWp50Gr78OWVmwYwf85jfh7Y5HnDGCb4q/IfuZbF679DVOqX1K\nxDIlKRLq1q1LKBTiiy++OOT61q1bAWjQoMGPum9RURFr166lcePG1K1b9+D1E//n05PCwkIA1q5d\nS7Vq1WjatOnB56SmplKnTp2Dz/k+o0aNIjEx8UfNKUlSpJVVdiwpKWH16tVRmig2xMOa5dNPoVGj\nH/NTSJL0w0VjzeLROZIO17o1LF4MY8aEvy0csOuvDzHx9HvY/Odz6fZUDjuLdgaeKUmSYsBxx0F+\nPjz44KFn3UTAKaeEyyZz54aP0vn2CwBj247l5+f8nKxnsvhsh8dASKpYkpOTadq0KWvWHHrM15o1\na0hNTaVx48Y/6r4JCQnMmDGD5cuXH3J9/fr1ABx//PEA5OfnM2vWrEO+NfX111/z+eefH3yOJElS\nPKxZPDpHkhTrLJpIKtu558ILL8Dw4eFPWQJ2660hxp74CB+/fQo9Z/Rlz749gWdKkqQY0KQJLF8O\nt9wCs2ZF9NYnnACvvRb+dcUVUFISvn79eddzSatLyJqRxdZdWyOaKUlHq1evXvz9739n2rRpvPfe\neyxYsIC8vDxycnJITk5m7969bNy4kW+++eaI75mcnEyPHj14/fXXWbhwIR988AH5+fk888wztGjR\ngtNPP/1g9r/+9S8ef/xx1q9fz+rVq7n//vupUaMG2dnZQf3IkiSpEor1NYtFE0lSrLNoIum7ZWXB\nU09B//7wzjuBRoVC8LvfJjKq1nTW/aUmfZ8dRHFJcaCZkiQpRpx2GixZEj6Tb9GiiN66bl145RV4\n//1w/7b4f5Yn/9Xlv+hxSg+6P9Odr/d8HdFMSToazZo1Y8yYMWzZsoVHHnmEt99+m0GDBtG9e3cA\nPvnkE6ZMmcK6det+0H179+7N0KFDeffdd5k6dSorVqygU6dOXHPNNQef07x5c37+85+zY8cOHnvs\nMZ5//nlOPvlkbrjhBtLS0iL6c0qSpMot1tcsmzZZNJEkxbakaA8gqYLr3x927ICcHFi5Elq0CCwq\nFIIH709mz9jneeEvvRlS5RLmDJ1FUoJ/VUmSpO/Rti289BIMGADz5kHnzhG7dXo65OVBv34wcCC8\n+CJUrRri/p73c8XCK7hg1gXkjcijRpUaEcuUpKNR1tnM32rWrBmPPvrod762ffv2tG/f/rDroVCI\nzp070/l7/n5t3rw5zZs3/0HzSpKk+BSra5aiIti61aKJJCm2uaOJpO83ciTceitkZ8M//hFoVCgE\n0x6uSp9d88n/82dc+tKVlB4o/f4XSpIkde4MM2eG2yBvvx3RW9eoEd40JRSCXr3gm28gIZTA430e\np1GtRvSb3Y+9+/dGNFOSJEmSVPls3gzHHgupqdGeRJKk4Fg0kXRkxo2DsWPDx+l8/nmgUQkJMOOP\nNcjeupQFf1rLuMXXcuDAgUAzJUlSjOjVCx5+OPz7e+9F9NZVq8LcueE3DHv0gMJCSExI5JkBz5Ca\nlMrgOYPZV7IvopmSJEmSpMrFY3MkSfHAoomkI3fTTeFvCHfvDl99FWhUYiI8Pz2dDv94mRmr8vhl\n/i2B5kmSpBgydChMnhxes3z8cURvXaUKzJoFp54K3brBl19ClcQqzLloDjuLdzJq/ihKSksimilJ\nkiRJqjw+/dSiiSQp9kWkaPLMM8+wcePGSNxKUkUWCsFdd0H79pCTAzt3BhqXnAzzn63LWe/n84dX\nZvHb1+4KNE+SJMWQq66CCRPCu7Ft3hzRWyclwVNPQdu20KULbNkCqcmpLBy6kI+//pgxi8e4G5sk\nSZIkxSmLJpKkeBCRosmGDRuYMmUKt912G8uWLaOwsDASt5VUEYVC4e3omzSBfv1g795A41JSYOns\n42ldkM/k5Q8ydfXDgeZJkqQYMmkSDB8O2dmwbVtEb52QEF4SZWVBp07hLktaShq5F+eyevNqJi6f\naNlEkiRJkuLQl19C3brRnkKSpGBFpGjym9/8hl/84heceuqpLFu2jBtvvJE//OEPvPPOO5SUuG20\nFHMSE2HGDKhWDYYMgX37Ao2rVg3yXmjCT1bnMWnJ7UwveCbQPEmSFEMmT4auXaFnT9ixI6K3DoXg\n3nth0CDo2BH+8Q+onVqbvBF5LN6wmP9a+V8RzZMkSZIkVXyFhVCrVrSnkCQpWBEpmgCceuqpjBgx\ngilTpjB69GiSkpKYPn06kyZN4rnnnmNzhLerlhRlyckwZw5s3w6jR0NpaaBxNWrAyhdbcvIbufx0\n3rW89P68QPMkSVKMCIXgwQehRQvo0wf27In47SdPDi+HOnaEv/0N6teoT/7IfJ4seJL73rovonmS\nJEmSpIrNookkKR5ErGjyrSpVqtC0aVOaNm1KgwYN2L17N2+//Ta/+c1vePDBB/n6668jHSkpWlJT\nYdEi+PBDGDcOAt4evlYtWPXCmRz/2gKGP38ZL3+0PNA8SZIUIxIS4Kmn4JhjwtuPFBdHPOJXv4Kf\n/zx8jM7770OjWo3IH5HP3W/ezePvPB7xPEmSJElSxbR9u0UTSVLsS4rUjfbu3cuaNWv405/+xIYN\nG0hJSeGss85i2LBhNG7cmI0bN/LHP/6RadOmccMNN0QqVlK01awJubnhT1VuugnuvDPQuGOPhTdn\nd+DMwc/TnyHkXbaIDo06BJopSZJiQFISzJ4NvXvDyJHw7LPh4wAjaOJEqFoVunSB5cuhdeumLL9k\nOV1ndKVGlRoMazUsonmSJEmSpIqnsBDS06M9hSRJwYpI0eSJJ56goKCAffv2ccoppzBq1CgyMzNJ\nSUk5+JwmTZpw7rnnkp+fH4lISRVJnTqQlwcdOoRX0AGXyerXhz89250zL3mS7qF+rLoqj8yGmYFm\nSpKkGFC1KsyfD1lZMHYsPPZY+OybCLrmmnBMt27w8suQmdmKJcOX0HNmT2pUqUGfZn0imidJkiRJ\nqlg8OkeSFA8iUjT54IMP6Nq1K+3bt6d+/frf+bxmzZpxwgknRCJSUkVz3HGQnw/nnx9eRY8ZE2jc\nCSfAn54awJmX7aJTqCerx75Ky7otA82UJEkxoEYNWLoUOneGSZPg7rsjXja5/HKoUgW6d4clS+Cc\nc85m3pB59H++P3MHz6Vr464RzZMkSZIkVRwWTSRJ8SAiRZO77rqLhISE731es2bNIhEnqaJq0iS8\nT3znzuEjdYYPDzSucWN469FLaHv1Ts4LZfPOuNdpckyTQDMlSVIMqF07vGY5//zwbmy/+lXEI0aM\nCJdNLrgAFi6ETud14tmBzzLohUEsvXgp555wbsQzJUmSJEnRZ9FEkhQPIlI0WbJkCaHv+BZgKBQi\nJSWFevXq0bJlS5KSIhIpqaI67bTwt4R79IC0NOgT7PbwzZrBGw+M5dxf7ODchG68O34Vx9c8PtBM\nSZIUAxo0CO/G1moDCoYAACAASURBVKFD+B3A8eMjHjFkCCQnh5dD8+bBBZ0u4LHej9F7Vm/yR+aT\n0SAj4pmSJEmSpOgpLoa9ey2aSJJiX0RaH6tXr+brr7+mpKSEhIQEqlevzq5duygtLT3keQ0aNGDi\nxImkpaVFIlZSRdW2Lbz0EgwYEP69S5dA41q1gpV33MD5t+/gnMQs3h3/GnWr1w00U5IkxYCTToK8\nPOjUKfwu4MiREY8YODBcNunfH158ES7qdhHfFH9Dz5k9WXnpSprVcddHSZIkSYoVhYVQtWp4h0tJ\nkmJZRIomffv2ZdasWVx66aWceeaZJCQkUFpayl//+ldmzpzJsGHDaNiwIY8//jjz5s1jZABv4Eqq\nYDp3hpkz4cIL4eWXw+WTAJ11FuT/cjLd7tlBu8Qe/GX8CtKrpgeaKUmSYkDz5rBsGWRlhXdjGzAg\n4hF9+sCsWTBoEMyeDaN7jGZn8U6ynsli1ehVnJR+UsQzJUmSJEnlb/v28AmtkiTFuoRI3GTx4sX0\n7duXtm3bkpAQvmVCQgIZGRn07duXhQsXctxxx3HBBRfw3nvvRSJSUmXQqxc8/DBccAGUw//3zzsv\nxOJxv+fTv7Tm/Ed6s6t4V+CZkiQpBrRpAwsWwGWXhXc4CUBODsyZA0OHwpIl8LNzfsZPz/wp3WZ0\n4/OdnweSKUmSJEkqX4WFHpsjSYoPESmafPXVV9SvX7/Mx2rXrs22bdsASE9PZ9cuP/iV4srQoXDH\nHdC9O3z8ceBxWd0SmDPij3z4TgO6TBtA0f6iwDMlSVIM6NABnnsOhgyBt94KJCIrK3yq4CWXhHst\nN59/MwNbDKT7zO58ufvLQDIlSZIkSeXHookkKV5EpGjSsGFDXn/99TIfe/PNN2nQoAEAW7duJd09\nw6T4c9VVMGFC+NOVzZsDj+vbO4npfWdRsCaRnCeGsr90f+CZkiQpBvTsCdOmhc+6Wbs2kIguXcIl\nk9GjYd68EHdl3UWHEzvQ89me7CjaEUimJEmSJKl8WDSRJMWLiBRN+vbty9q1a5k8eTJLly7l9ddf\nZ8mSJdxxxx28++679OnTh02bNjF37lzatGkTichA7N+/n/vvv59169ZFexQp9kyaBMOHQ3Y2fPFF\n4HHDBlfh4U5zWbXmSwZOH03pgdLAMyWpvLhmkQI0aBDcfTf06AEbNgQS0bEjLFoEV14JL74Y4qFe\nD9Hs2Gb0fa4ve/btCSRTkiRJkhQ8iyaSpHiRFImbtGrVimuvvZaFCxeyaNEiDhw4QGJiIqeccgoT\nJ07k1FNPZe3atbRt25Z+/fpFIjLiNm3axMyZM/n8c89HlwIzeXJ4pd2zJ6xYEfiK+4pR1di5azE3\nvNOVESnjmDnsIUKhUKCZkhQ01yxSORg9GnbsCBdkX38dGjWKeMR558GSJdCrF5SWJvDUoKcYNGcQ\ng+YMYt6QeVRJrBLxTEmSJElSsCyaSJLiRUSKJm+99RbNmzdn0qRJ7Nu3j927d5OWlkZCwr83TDnj\njDM444wzIhEXiJUrV9K3b19efvnlaI8ixa5QCB58EC69NLwl/bJlUK1aoJETrq7JznuWMfnPnUiv\nehMPDbwz0DxJCpprFqmc/PznsH37v8sm9epFPOLccyE3Fy64AEpKknl+8PP0ntWbEfNGMGvgLBIT\nEiOeKUmSJEkKzvbtFk0kSfEhIkfnzJo1i3/84x8AJCcnU6tWrUNKJpXBiBEjOP3006M9hhT7EhLg\nySfh2GPhoouguDjwyFt/UYfxx+Qx7c0XuGmpRRNJlZtrFqkc3XpruAXSo0f43cIAnH12uHv7s5/B\ni7OrMn/ofDYVbuKqRVdx4MCBQDIlSZIkScEoLIT09GhPIUlS8CLSBjnmmGPYu3dvJG71g3z99ddc\ne+21bCjj7PT169fz29/+lvHjx3PzzTeTl5dX7vNJ+g5JSfDcc1BUBCNGQElJ4JH33HocoxPzuXvl\nQ/xuxdTA8yTpf3PNIlVSoRDcey+0aRM+42bXrkBizjoLli+HCRNg7nM1WDp8Ke98/g7XvXydZRNJ\nkiRJqkQ8OkeSFC8icnROx44dmT17Nh999BEnnngiKSkphz2nXbt2kYg66KuvvuLBBx8ss+CyceNG\npk6dStu2benfvz9/+9vfmDt3LiUlJfTs2ZOFCxfy17/+9eDsHTt2jOhsko5A1aowf354O/oxY2Da\ntPCHOQEJheCx3zVm58/zuCW/M+mpNRnTbmRgeZL0LdcsUiWXkBBepwwdCgMGwKJFUMa/d45WZma4\nbNK9Oxw4cAwvX/IyHZ/uSK2qtbi98+0Rz5MkSZIkRZ5FE0lSvIhI0eTFF18E4I033vjO50SqaHLg\nwAHeeuutg5llWbRoEY0aNWL06NEAtGzZkpKSEnJzc+nWrRt9+/alb9++EZlH0lGoUQOWLIHOnWHS\nJLj77sDLJs8+0IJvxuQyfnE2aSnVuTjzwsDyJMU31yxSDElKgmefhb59YdgweOGF8LUIa9MG8vLC\nZZPS0vrkj8jn/KfOJ61KGhPbT4x4niRJkiQpsiyaSJLiRUTeHZ08eXIkbnNEPvvsM2bNmkXnzp1p\n3rw5U6ceegTGvn372LBhw2EfymRmZrJ8+XI++ugjWrRoUW7zSvoetWuHv757/vlwzDFw882BxiUk\nwLyHM+lxxUIufak3aVVr0Ldlj0AzJcUn1yxSjElJgZdegh494Mor4YknwguLCMvICJdNsrPhwIET\nyR+ZT8enOpKWksZVZ14V8TxJkiRJUuRYNJEkxYuIFE3q1KlzyJ/37dtHYmIiCQG88Vq7dm0mT55M\neno6H3744WGPb9u2jZKSEurXr3/I9bp16wKwZcuW//ihzcSJflNQKncNGkB+PnToADVrwvjxgcYl\nJUHutPPoOPoFLnxuMMsvXUSXUzoEmikp/rhmkWJQ9erh3di6dIEJE+CBBwLZje2MM/5dNrmTU1k+\nYjldpnchrUoaw1oNi3ieJEmSJCkyLJpIkuJFxPZ7/te//sXChQt5//332bNnD7/85S954403aNCg\nAV27do1UDNWrV/+Pj+/ZsweAqlWrHnL92z/v3bs3YrMATJ8+/bBCTUZGBhkZGRHNkWLeSSeFP1Hp\n1ClcNhk1KtC4KlXg1SeyOXvkk/R8uh+rfppH2xMyA82UykNBQQEFBQWHXCstLY3SNPHNNYsUo2rV\ngmXLoGNH+PWv4fbbA4k544xwDzc7G+44cDpLhy+lx8we1KhSgz7N+gSSKZUn1yySJEmKRdu3Q3p6\ntKeQJCl4ESmafPrpp9xzzz2kpaVx9tlns3LlSgCSk5N54YUXqFq1Ku3bt49E1Pc6cODAf3w8FOFv\nHI4aNYrExMSI3lOKW82bQ25u+BOVtDQYODDQuKpV4c0nB9Bm1Dd0nNaTv1yzktPqe0yFKreyigMl\nJSWsXr06ShPpu7hmkSqxevUO3Y3tuusCiWndOhyTlQV30JZ5Q+bR//n+zB08l66NI1fml6LBNYsk\nSZJikTuaSJLiRUTOtnnxxRc56aST+PWvf83gwYOB8IcjF110Eeeddx4rVqyIRMwRSU1NBQ7/FvC3\nf/72cUkVVGYmLFgAl18e/mQlYDVqwNtPjKDOe7dzzkPZbPzq74FnShK4ZpEqvRNOCO/Gdvfd8MQT\ngcW0ahVeEt18M/wtvxPPDnyWQS8MYvVnfhgvSZIkSRXJ3r1QXBz+PoIkSbEuIkWTjRs30q1btzK/\nJXvWWWexZcuWSMQckbp16xIKhfjiiy8Oub5161YAGjRoUG6zSPqROnSA2bNh8GB4663A49LT4d1p\nV1P9v8eR+ftubN7xz8AzJck1ixQDmjaFl1+GG2+EOXMCi/nfZZN/rryAR3s/Su/nevPXLX8NLFOS\nJEmS9MMUFkK1apCcHO1JJEkKXkSKJsnJyRQXF5f52O7du0kux/+qJicn07RpU9asWXPI9TVr1pCa\nmkrjxo3LbRZJR6FHD5g2Dfr0gbVrA4+rUwfe/cONhNYPoc392WzbvS3wTEnxzTWLFCNat4ZFi+Cn\nP4VlywKLadUqvIHKTTfBzj8N5s5ud9JjZg82fLkhsExJkiRJ0pHz2BxJUjyJSNGkZcuWLFq0iK++\n+opQKHTw+t69e1m+fDnNmzePRMwR69WrF3//+9+ZNm0a7733HgsWLCAvL4+cnJxyLb1IOkqDBoW3\no+/RAzYE/yHKccfBmim/Zff6zrS5ryeFewsDz5QU31yzSDHi3HPDO5oMGwavvx5YTOvW4Z1NfvlL\nSCi4guvbX0/2M9lsKtwUWKYkSZIk6chYNJEkxZOIFE0GDhxIUVERt912G/fccw8AL774Irfeeitf\nffUVAwYMiETMEWvWrBljxoxhy5YtPPLII7z99tsMGjSI7t27l+sckiJg9OjwdvRZWbAp+A9RGjcO\n8Zf/+gPb1rfkrPt7s3vf7sAzJcUv1yxSDOnWDZ5+Gvr3h/+zU1EktW4d3tnkxhsh/YMJXJZxGVkz\nstjyTfkdVypJkiRJOtz27eFj2iVJigdJkbhJ7dq1ueWWW8jPz+eDDz6gbt26FBUVcfbZZ5OdnU2t\ngCqczZo149FHHy3zsYyMDDIyMgLJlVTOrr02XAfPzg5/S7hevUDjmjdL4I3rn6TdfYNp98BA3r5u\nIVUSqwSaKSm2uWaR4kS/fvDAA9CzJ6xcCS1aBBJzxhnhskl2Ntx11630/kkh3Wd259VRr3JM6jGB\nZEqSJEmS/jN3NJEkxZOIFE0AatSoQf/+/SN1O0k61K23hivh3bvDq68GXg3PzEhixdXP0XlaH7r8\n4WJW/uw5khIi9lemJEmKVSNG/Lsgu2oVnHxyIDFnnAHLl0N2doh77rmXncddRc6zOeSPzKdGlRqB\nZEqSJEmSvptFE0lSPInYp6a7d+/mww8/pKioiAMHDhz2eLt27SIVJSkehUJw771wxRXQq1f4k5Xq\n1QONPO/cFJbsnccFz3Wn92NXsXTMH0kIReTEMUmSFMvGjQu/w5iVFd6NrWHDQGIyMsJLou7dQ9x7\n36PsTL+YfrP7sWT4EqomVQ0kU5IkSZJUNosmkqR4EpGiyX//93/z6KOPsm/fvu98TqwWTaZPn05m\nZqZb3kvlISEBHn8chg6FAQNg0SJISQk0snvn6jy/awlDlnZhyJMTeOGyBwiFQoFmSpFUUFDAmjVr\noj2GKgDXLFI5u+mm8LuM3buHj9GpXTuQmDZt4OWXoUePRO59YAYvJA1k8JzBzB08l+TE5EAypSC4\nZpEkSVJlZ9FEkhRPIlI0mTdvHg0bNuSiiy4iPT09rj6EHTVqFImJidEeQ4ofiYkwcyb06wfDhsEL\nL0BSsEfaXNgrncd3v8wVqzpy1XO38fjw/wo0T4qkjIwMWrVqxerVq6M9iqLMNYtUzkIhuOuu8DuN\nOTmQnw9paYFEZWbCsmXQo0cV7ntwDk8VX8ClCy7lmQHPuBubKg3XLJIkSarsCguhTp1oTyFJUvmI\nyLuOn3/+OX379qVp06bUrVuXOnXqHPZLkiImJQXmzoWtW+HKK6G0NPDI0RfV4/7MfJ58Zwa/eOme\nwPMkSVIMCIXg4YehSRPo3x/27g0s6swzITcXrvtZKqNTFvK3L//G1UuuLvNYU0mSJElS5BUWQnp6\ntKeQJKl8RKRoUrt2bfYG+KapJB2menVYvBgKCmDCBCiHD1F+NuoEbm+Sz/1/uo/JudMCz5MkSTEg\nMRFmzIDU1PDxf//huNGj1bYtLFkCE65JY2xaLqs2reKG/Bssm0iSJElSOdi+3aNzJEnxIyJFk549\ne7JkyRK2bdsWidtJ0pFJT4eXXw7/uv32com85ZpTmVBnObe9djMPrZxdLpmSJKmSS06GOXPg669h\n9OhAd2M75xxYtAgmXn0sE+rk8dL7L3HnqjsDy5MkSZIkhRUWWjSRJMWPpEjc5O2332b79u386le/\nIi0tjeTk5EMeD4VC3HHHHZGIkqRD1asHeXnQoUO4eDJhQuCR91x/OttvW8rPXu5JzdQajDi7d+CZ\nkiSpkktNDTdAunaFcePgoYfCR+sEoH17WLgQ+vZtyF2P5fNffzmfmik1GXf2uEDyJEmSJEkWTSRJ\n8SUiRZP09HTSPXhOUrSceCLk50PHjlCzJlx+eeCRj9/elh3Xv8ToBf1JS5lL/zO6Bp4pSZIquZo1\nYdky6NQJbr4ZfvvbwKI6dID586F//5P57bQ8bnutE2lV0hiVMSqwTEmSJEmKZxZNJEnxJCJFk0sv\nvRSAf/7zn7z//vsUFhbSpUsXtm3bxgknnEBqamokYiTpuzVtGj5Cp2vX8Ic4F10UaFwoBM9P6UTO\nz2Yy6IVBLE/NpetPzgk0U5IkxYA6df69G1utWnDDDYFFdewIc+fCwIHNmfzEMq5bnkVaShoDWwwM\nLFOSJEmS4pVFE0lSPIlI0aS0tJSZM2fy5ptvHrx25plnsnTpUrZu3covfvELjjnmmEhESdJ3a90a\nFi+GCy6AGjUgJyfQuFAIljzQi45XP0LP6b1546craNuoVaCZkiQpBhx3XHg3tvPPD78LOWZMYFFd\nusCcOXDRRW247YmFXLGwD9WTq9Pj1B6BZUqSJElSvDlwIFw0cfN/SVK8SIjETZYsWcKf//xnRowY\nwZQpUwAIhUIMGjSIAwcOMH/+/EjESNL3O/fc8KcpF18Mr78eeFxiIrw6dQin/etOzn+sO//9r78F\nnilJkmJAkyawfDnceivMmhVoVFYWPPcc/Pry87jx1NkMmzuMNza9EWimJEmSJMWTPXtg377wZtuS\nJMWDiBRN3nzzTfr06cN5551H9erVD14//vjj6dOnD+vXr49EjCQdmW7d4MknoX9/WLMm8LjkZHjr\noSto9Nkkzv5DFn//6tPAMyVJUgw47TRYsgTGjYNFiwKN6tkTZs6E313ZnetO/SN9Z/dlzefBr5Mk\nSZIkKR4UFoY32U5MjPYkkiSVj4gUTXbs2EGjRo3KfCw9PZ3du3dHIkaSjlz//vDAA+Hjc95/P/C4\nqlXh3Yevo/anl5Jxbxb/2rk18ExJkhQD2raFl16CkSPhlVcCjerVC55+Gu67ciBXN7mfnGdzeP+L\n4NdJkiRJkhTrCgvDJ6NKkhQvIlI0qVu3LuvWrSvzsb/97W/Uq1cvEjEV0vTp0ykoKIj2GJLKMmJE\neDv67Gz4+98Dj6teHf76+9tJ+TSHVnf14Os92wPPlL5PQUEB06dPj/YYqgBcs0gVWOfO4e1GLrwQ\n/vznQKP69oU//hEe/ulIRjS6hexnsvnH9n8EmikdCdcskiRJqswsmkiS4k1EiiZZWVmsWLGCWbNm\n8f7/7BywZcsWli9fzvLly+ncuXMkYiqkUaNGkZGREe0xJH2Xa66BsWPDZZPPPw887phjQqy75z72\nfdqGVr+7gG+Kvwk8U/pPMjIyGDVqVLTHUAXgmkWq4Hr1gocfDv/+3nuBRg0cCI88Ak9fPY5+x11N\n1owsPt8Z/DpJ+k9cs0iSJKkys2giSYo3SZG4SYcOHdi5cydLlizhtddeA+CJJ54gMTGRHj160KlT\np0jESNKPc9NNsH07dO8OK1dC7dqBx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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first column plots the energy gap over $V_1$, $U$, and $b/a$ for $P_0=1$, the second for $P_0=0$ (no input polarization). We have plotted $\\Delta E$ over $V_1$ for $b/a = 100$ and $b/a=2$. We set $U = 10^6$ except for the $\\Delta E$ over $U$ plot.\n", "\n", "Evidently, a biasing external potential (i.e. breaking the $P=\\pm1$ symmetry) changes the functional form of the $V_1$ dependence. With $P_0 = 1$ we have $\\Delta E \\sim \\frac{1}{V_1^3}$, whereas for an isolated cell ($b/a \\rightarrow \\infty$) or for a close-by static charge not introducing bias ($P_0 = 0$, $b/a = 2$), we have $\\Delta E \\sim \\frac{1}{V_1}$. Contrary to our expectation, the $U$ dependence is very weak and does not matter. Lastly, a smaller $b/a$ (meaning a higher Coulomb potential) also decreases the singlet-triplet splitting.\n", "\n", "Quite generally, a higher overall Coulomb potential (larger $V_1$, smaller $b/a$) seems to decrease the energy gap between singlet and triplet states. A biasing external potential decreases the gap further.\n", "\n", "The bond approximation should work, as long as the singlet-triplet splitting (which it neglects) is \"washed-out\", that is, as long as the temperature is much larger than the energy gap between singlet and triplet. As a very, very rough estimate we could say $T \\gg \\frac{t^2}{V_1}$. The bond approximation should work better, the higher the overall Coulomb potential.\n", "\n", "As a last step, we look at the low energy spectrum and the polarization over temperature for two cases, one where the approximation arguably does not work very well, and the other where it does. This is for a two cell system." ] }, { "cell_type": "code", "collapsed": false, "input": [ "s_f = qca.QcaFixedCharge()\n", "s_b = qca.QcaBond()\n", "\n", "def computeHistogramAndPolarization(V1,boa):\n", " # Wire geometry\n", " N = 2\n", " P_0 = 1\n", " \n", " # Other parameters\n", " V0 = 1E6\n", " \n", " # Set the systems up\n", " s_f.l = qca.Wire(N,V1,boa,P_0)\n", " s_b.l = qca.Wire(N,V1,boa,P_0)\n", " s_f.V0 = V0\n", " s_b.V0 = V0\n", " s_f.init()\n", " s_f.run()\n", " s_b.init()\n", " s_b.run()\n", " \n", " # Calculate energy histogram\n", " Es_b = np.array(s_b.energies())\n", " Es_f = np.array(s_f.energies())\n", " Emin = np.concatenate((Es_b, Es_f)).min()\n", " Es_b -= Emin\n", " Es_f -= Emin\n", " Emin = 0\n", " #Emax = np.concatenate((Es_b, Es_f)).max()\n", " Emax = 4\n", " bins = np.arange(Emin,Emax,1E-4)\n", " h_f,_ = np.histogram(Es_f,bins)\n", " h_b,_ = np.histogram(Es_b,bins)\n", " bins = bins[:-1]\n", " \n", " # Calculate polarization over temperature\n", " Ps = []\n", " for T in np.linspace(0.0001,Emax,200):\n", " beta = 1/T\n", " s_f.beta = beta\n", " s_b.beta = beta\n", " s_f.run(True)\n", " s_b.run(True)\n", " Ps.append([T, s_f.results['P'][1],s_b.results['P'][1]])\n", " Ps = np.array(Ps)\n", " \n", " return (bins,h_f,h_b,Ps)\n", "\n", "bins1,h_f1,h_b1,Ps1 = computeHistogramAndPolarization(20.0,2)\n", "bins2,h_f2,h_b2,Ps2 = computeHistogramAndPolarization(100.0,2)\n", "\n", "fig = plt.figure(figsize=(5,5))\n", "\n", "p = fig.add_subplot(2,2,1)\n", "p.plot(bins1,h_f1)\n", "p.plot(bins1,-h_b1)\n", "p.set_xlim((-0.1,4))\n", "p.get_yaxis().set_ticklabels([2,0,2,4,6,8,10])\n", "p.set_ylabel('state count')\n", "p.set_xlabel('energy')\n", "p.set_xticks(range(5))\n", "#p.set_title('$V_1 = 20$')\n", "p.text(0.96,0.96, '$V_1 = 20$',\n", " horizontalalignment='right', \n", " verticalalignment='top', \n", " transform=p.transAxes)\n", "p.text(0.03,0.03,'(a)', \n", " horizontalalignment='left', \n", " verticalalignment='bottom', \n", " transform=p.transAxes)\n", "\n", "p = fig.add_subplot(2,2,2)\n", "p.plot(Ps1[:,0],Ps1[:,1],label='Fixed')\n", "p.plot(Ps1[:,0],Ps1[:,2],label='Bond')\n", "p.legend()\n", "p.set_xlabel('temperature')\n", "p.set_ylabel('polarization $P_2$')\n", "p.set_xticks(range(5))\n", "#p.set_title('$V_1 = 20$')\n", "p.text(0.96,0.74, '$V_1 = 20$',\n", " horizontalalignment='right', \n", " verticalalignment='top', \n", " transform=p.transAxes)\n", "p.text(0.03,0.03,'(b)', \n", " horizontalalignment='left', \n", " verticalalignment='bottom', \n", " transform=p.transAxes)\n", "\n", "p = fig.add_subplot(2,2,3)\n", "p.plot(bins2,h_f2)\n", "p.plot(bins2,-h_b2)\n", "p.set_xlim((-0.1,4))\n", "p.get_yaxis().set_ticklabels([2,0,2,4,6,8,10])\n", "p.set_ylabel('state count')\n", "p.set_xlabel('energy')\n", "p.set_xticks(range(5))\n", "#p.set_title('$V_1 = 100$')\n", "p.text(0.96,0.96, '$V_1 = 100$',\n", " horizontalalignment='right', \n", " verticalalignment='top', \n", " transform=p.transAxes)\n", "p.text(0.03,0.03,'(c)', \n", " horizontalalignment='left', \n", " verticalalignment='bottom', \n", " transform=p.transAxes)\n", "\n", "p = fig.add_subplot(2,2,4)\n", "p.plot(Ps2[:,0],Ps2[:,1],label='Fixed')\n", "p.plot(Ps2[:,0],Ps2[:,2],label='Bond')\n", "p.set_xlabel('temperature')\n", "p.set_ylabel('polarization $P_2$')\n", "p.set_xticks(range(5))\n", "p.set_yticks([0,0.2,0.4,0.6,0.8])\n", "#p.set_title('$V_1 = 100$')\n", "#p.legend()\n", "p.text(0.96,0.96, '$V_1 = 100$',\n", " horizontalalignment='right', \n", " verticalalignment='top',\n", " transform=p.transAxes)\n", "p.text(0.03,0.03,'(d)',\n", " horizontalalignment='left', \n", " verticalalignment='bottom', \n", " transform=p.transAxes)\n", "\n", "#fig.subplots_adjust(wspace=0.4,hspace=0.4)\n", "fig.tight_layout()\n", "fig.savefig('../plots/chapter02/bond_approximation2.pdf')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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97x/+oP9zsWXLFowfPx6enp7atmvXrmm/QPTr1087J7nGlStXIJPJtCMzrcVJWUxLgFMA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\nJiaSn5+vYlxE7jrNmjUjJSWFuLg42rRpQ8uWLVmyZAk5OTlMnz6dwMBAA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"text": [ "" ] } ], "prompt_number": 28 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here it is instructive to look at the qualitative agreement between the fixed charge and the bond spectra. In the first case ($V_1 = 20$) they don't look anything alike, the bond approximation does not work very well in this regime. In the second case they do look similar, although the bond approximation does not resolve all the lines in the fixed charge spectrum. Here the approximation works much better, as apparent in the polarization over temperature graph.\n", "\n", "It is worth noting that the ground state of the bond approximation can be qualitatively completely wrong, as seen in $V_1 = 20$ polarization plot. However, even in this case, for higher temperatures ($T > 1$) the curves agree suprisingly well. The bond model reproduces the most populous energy states and apparently that's enough to give (almost) correct results at higher temperatures. The lower the temperature the more important the few lowest lying energy states become, which the bond model misses. \n", "\n", "Lastly, notice that for the two cell system each bond state corresponds to $16$ ($4 \\cdot4$) fixed charge states." ] } ], "metadata": {} } ] }