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faucon/Kwant QZ iteration failed.ipynb

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QZ iteration Error in kwant
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Kwant QZ iteration failed.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from __future__ import print_function, division\n",
"\n",
"import kwant\n",
"\n",
"import numpy as np\n",
"from numpy import sqrt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Define the system"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"HZ = sqrt(6) / 6.0\n",
"h = 1 / (sqrt(3) * 4)\n",
"lat = kwant.lattice.general([(1, 0, 0), (0.5, -sqrt(3) * 0.5, 0), (0, 1 / sqrt(3), 2 * HZ)],\n",
" [(0, 0, 0), (0.5, 0, 0), (0.25, -0.25 * sqrt(3), 0), (0.25, -h, HZ)])\n",
"\n",
"def make_latticeperiodic_pyrochlore_slab(t_1, t_2, t_perp, lambda_1, lambda_2, shape=(5, 4, 2)):\n",
" \"\"\"\n",
" create a pyrochlore slab in a parallelepiped shape,a s given by the lattice vectors\n",
" with periodic boundary conditions along the second lattice vector\n",
" and leads attached at tle left and right (x direction)\n",
" \"\"\"\n",
" a, b, c, d = lat.sublattices\n",
"\n",
" def initialize_hopping(sys):\n",
" # construct all hoppings with SO explicit\n",
" sys[kwant.HoppingKind((0, 0, 0), b, a)] = t_1 + 1j * lambda_1\n",
" sys[kwant.HoppingKind((-1, 0, 0), b, a)] = t_1 - 1j * lambda_1\n",
"\n",
" sys[kwant.HoppingKind((0, 0, 0), c, a)] = t_1 - 1j * lambda_1\n",
" sys[kwant.HoppingKind((0, -1, 0), c, a)] = t_1 - 1j * lambda_1\n",
"\n",
" sys[kwant.HoppingKind((0, 0, 0), c, b)] = t_1 + 1j * lambda_1\n",
" sys[kwant.HoppingKind((1, -1, 0), c, b)] = t_1 + 1j * lambda_1\n",
"\n",
" # construct all NNN hoppings with SO explicit\n",
" sys[kwant.HoppingKind((0, -1, 0), b, a)] = t_2 - 1j * lambda_2\n",
" sys[kwant.HoppingKind((-1, 1, 0), b, a)] = t_2 - 1j * lambda_2\n",
"\n",
" sys[kwant.HoppingKind((-1, 0, 0), c, a)] = t_2 + 1j * lambda_2\n",
" sys[kwant.HoppingKind((1, -1, 0), c, a)] = t_2 + 1j * lambda_2\n",
"\n",
" sys[kwant.HoppingKind((0, -1, 0), c, b)] = t_2 - 1j * lambda_2\n",
" sys[kwant.HoppingKind((1, 0, 0), c, b)] = t_2 - 1j * lambda_2\n",
"\n",
" nn_hoppings = lat.neighbors(n=1)\n",
" for hop in nn_hoppings:\n",
" # hoppings in z-direction\n",
" if hop.family_a == d or hop.family_b == d:\n",
" sys[hop] = t_perp\n",
"\n",
" # Build ancillary system with y-periodic BCs. This system cannot be\n",
" # finalized in Kwant 1.0.\n",
" sym = kwant.TranslationalSymmetry(lat.vec((0, shape[1], 0)))\n",
"\n",
" anc = kwant.Builder(sym)\n",
" anc[lat.shape(lambda p: 0 <= p[0] < shape[0] and 0 <= p[2] < shape[2], (0, 0, 0))] = None\n",
" initialize_hopping(anc)\n",
"\n",
" sys = kwant.Builder()\n",
"\n",
" sys[anc.sites()] = 0\n",
" for s1, s2 in anc.hoppings():\n",
" sys[sym.to_fd(s1), sym.to_fd(s2)] = anc[s1, s2]\n",
"\n",
" # leads\n",
" # TRICK ancestor only periodic in Y-direction to catch also the x-direction hoppings later on\n",
" anc_sym = kwant.TranslationalSymmetry(lat.vec((0, shape[1], 0)))\n",
"\n",
" anc_lead = kwant.Builder(anc_sym)\n",
" anc_lead[lat.shape(lambda p: -2 <= p[0] <= 2 and 0 <= p[2] < shape[2], (0, 0, 0))] = 0\n",
" initialize_hopping(anc_lead)\n",
"\n",
" # at the left\n",
" lead_symmetry = kwant.TranslationalSymmetry(lat.vec([-1, 0, 0]))\n",
" lead = kwant.Builder(lead_symmetry)\n",
"\n",
" lead[anc_lead.sites()] = 0\n",
" for s1 in anc_lead.sites():\n",
" lead[s1] = 1\n",
"\n",
" for s1, s2 in anc_lead.hoppings():\n",
" lead[s1, anc_sym.to_fd(s2)] = anc_lead[s1, s2]\n",
"\n",
" sys.attach_lead(lead)\n",
" # and right\n",
" sys.attach_lead(lead.reversed())\n",
"\n",
" sys.parameter = dict(t_1=t_1,\n",
" t_2=t_2,\n",
" t_perp=t_perp,\n",
" lambda_1=lambda_1,\n",
" lambda_2=lambda_2,\n",
" shape=shape,\n",
" peridoic=True)\n",
" return sys, lat\n",
"\n",
"\n",
"def make_periodic_pyrochlore_slab(t_1, t_2, t_perp, lambda_1, lambda_2, shape=(5, 4, 2)):\n",
" \"\"\"\n",
" create a pyrochlore slab in a rectangular shape\n",
" with periodic boundary conditions in y-direction\n",
" and leads attached at tle left and right (x direction)\n",
" \"\"\"\n",
" a, b, c, d = lat.sublattices\n",
"\n",
" def initialize_hopping(sys):\n",
" # construct all hoppings with SO explicit\n",
" sys[kwant.HoppingKind((0, 0, 0), b, a)] = t_1 + 1j * lambda_1\n",
" sys[kwant.HoppingKind((-1, 0, 0), b, a)] = t_1 - 1j * lambda_1\n",
"\n",
" sys[kwant.HoppingKind((0, 0, 0), c, a)] = t_1 - 1j * lambda_1\n",
" sys[kwant.HoppingKind((0, -1, 0), c, a)] = t_1 - 1j * lambda_1\n",
"\n",
" sys[kwant.HoppingKind((0, 0, 0), c, b)] = t_1 + 1j * lambda_1\n",
" sys[kwant.HoppingKind((1, -1, 0), c, b)] = t_1 + 1j * lambda_1\n",
"\n",
" # construct all NNN hoppings with SO explicit\n",
" sys[kwant.HoppingKind((0, -1, 0), b, a)] = t_2 - 1j * lambda_2\n",
" sys[kwant.HoppingKind((-1, 1, 0), b, a)] = t_2 - 1j * lambda_2\n",
"\n",
" sys[kwant.HoppingKind((-1, 0, 0), c, a)] = t_2 + 1j * lambda_2\n",
" sys[kwant.HoppingKind((1, -1, 0), c, a)] = t_2 + 1j * lambda_2\n",
"\n",
" sys[kwant.HoppingKind((0, -1, 0), c, b)] = t_2 - 1j * lambda_2\n",
" sys[kwant.HoppingKind((1, 0, 0), c, b)] = t_2 - 1j * lambda_2\n",
"\n",
" nn_hoppings = lat.neighbors(n=1)\n",
" for hop in nn_hoppings:\n",
" # hoppings in z-direction\n",
" if hop.family_a == d or hop.family_b == d:\n",
" sys[hop] = t_perp\n",
"\n",
" # Build ancillary system with y-periodic BCs. This system cannot be\n",
" # finalized in Kwant 1.0.\n",
" sym = kwant.TranslationalSymmetry(lat.vec((-shape[1] / 2, shape[1], 0)))\n",
"\n",
" # Define unit cell ('fundamental domain') to be along y-axis and not along lattice vector\n",
" for fam in (a, b, c, d):\n",
" sym.add_site_family(fam, other_vectors=[[-1, 0, 0], [-1, 2, 3]])\n",
"\n",
" anc = kwant.Builder(sym)\n",
" anc[lat.shape(lambda p: 0 <= p[0] < shape[0] and 0 <= p[2] < shape[2], (0, 0, 0))] = None\n",
" initialize_hopping(anc)\n",
"\n",
" sys = kwant.Builder()\n",
"\n",
" sys[anc.sites()] = 0\n",
" for s1, s2 in anc.hoppings():\n",
" sys[sym.to_fd(s1), sym.to_fd(s2)] = anc[s1, s2]\n",
"\n",
" # leads\n",
" # TRICK ancestor only periodic in Y-direction to catch also the x-direction hoppings later on\n",
" anc_sym = kwant.TranslationalSymmetry(lat.vec((-shape[1] / 2, shape[1], 0)))\n",
"\n",
" # Define unit cell ('fundamental domain') to be along y-axis and not along lattice vector\n",
" for fam in (a, b, c, d):\n",
" anc_sym.add_site_family(fam, other_vectors=[[-1, 0, 0], [-1, 2, 3]])\n",
"\n",
" anc_lead = kwant.Builder(anc_sym)\n",
" anc_lead[lat.shape(lambda p: -2 <= p[0] <= 2 and 0 <= p[2] < shape[2], (0, 0, 0))] = 0\n",
" initialize_hopping(anc_lead)\n",
"\n",
" # at the left\n",
" lead_symmetry = kwant.TranslationalSymmetry(lat.vec([-1, 0, 0]))\n",
" lead = kwant.Builder(lead_symmetry)\n",
"\n",
" # Define unit cell ('fundamental domain') to be along y-axis and not along lattice vector\n",
" for fam in (a, b, c, d):\n",
" lead_symmetry.add_site_family(fam, other_vectors=[[-1, 2, 0], [-1, 2, 3]])\n",
"\n",
" lead[anc_lead.sites()] = 0\n",
" for s1 in anc_lead.sites():\n",
" lead[s1] = 1\n",
"\n",
" for s1, s2 in anc_lead.hoppings():\n",
" lead[s1, anc_sym.to_fd(s2)] = anc_lead[s1, s2]\n",
"\n",
" sys.attach_lead(lead)\n",
" # and right\n",
" sys.attach_lead(lead.reversed())\n",
"\n",
" sys.parameter = dict(t_1=t_1,\n",
" t_2=t_2,\n",
" t_perp=t_perp,\n",
" lambda_1=lambda_1,\n",
" lambda_2=lambda_2,\n",
" shape=shape,\n",
" peridoic=True)\n",
" return sys, lat"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#lattice\n",
"sys, lat = make_latticeperiodic_pyrochlore_slab(\n",
" t_1=-1, t_2=0.3, t_perp=1, lambda_1=0.3, lambda_2=0.2, shape=(5,8,(4*2-1)*HZ))\n",
"\n",
"sys2, lat2 = make_periodic_pyrochlore_slab(\n",
" t_1=-1, t_2=0.3, t_perp=1, lambda_1=0.3, lambda_2=0.2, shape=(5,8,(4*2-1)*HZ))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"lattice_sys = sys.finalized()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"rectangle_sys = sys2.finalized()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# QZ iteration fails"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"ename": "LinAlgError",
"evalue": "QZ iteration failed to converge in zgges",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mLinAlgError\u001b[0m Traceback (most recent call last)",
"\u001b[1;32m<ipython-input-6-a3d46ac6196b>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mkwant\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msmatrix\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrectangle_sys\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1.5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtransmission\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[1;32m/home/maxtre/bin/anaconda/lib/python2.7/site-packages/kwant/solvers/common.pyc\u001b[0m in \u001b[0;36msmatrix\u001b[1;34m(self, sys, energy, args, out_leads, in_leads, check_hermiticity)\u001b[0m\n\u001b[0;32m 336\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 337\u001b[0m linsys, lead_info = self._make_linear_sys(sys, in_leads, energy, args,\n\u001b[1;32m--> 338\u001b[1;33m check_hermiticity, False)\n\u001b[0m\u001b[0;32m 339\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 340\u001b[0m kept_vars = np.concatenate([vars for i, vars in\n",
"\u001b[1;32m/home/maxtre/bin/anaconda/lib/python2.7/site-packages/kwant/solvers/common.pyc\u001b[0m in \u001b[0;36m_make_linear_sys\u001b[1;34m(self, sys, in_leads, energy, args, check_hermiticity, realspace)\u001b[0m\n\u001b[0;32m 171\u001b[0m \u001b[0mlead\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msys\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mleads\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mleadnum\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 172\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mrealspace\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 173\u001b[1;33m \u001b[0mprop\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstab\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlead\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmodes\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0menergy\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 174\u001b[0m \u001b[0mlead_info\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mprop\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 175\u001b[0m \u001b[0mu\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mulinv\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnprop\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msvd_v\u001b[0m \u001b[1;33m=\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m/home/maxtre/bin/anaconda/lib/python2.7/site-packages/kwant/system.pyc\u001b[0m in \u001b[0;36mmodes\u001b[1;34m(self, energy, args)\u001b[0m\n\u001b[0;32m 211\u001b[0m \u001b[1;31m# Subtract energy from the diagonal.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 212\u001b[0m \u001b[0mham\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mflat\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m:\u001b[0m\u001b[0mham\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m-=\u001b[0m \u001b[0menergy\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 213\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mphysics\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmodes\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mham\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minter_cell_hopping\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 214\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 215\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mselfenergy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0menergy\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m/home/maxtre/bin/anaconda/lib/python2.7/site-packages/kwant/physics/leads.pyc\u001b[0m in \u001b[0;36mmodes\u001b[1;34m(h_cell, h_hop, tol, stabilization)\u001b[0m\n\u001b[0;32m 581\u001b[0m \u001b[0mmatrices\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mv\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mextract\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msetup_linsys\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mh_cell\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mh_hop\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtol\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstabilization\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 582\u001b[0m \u001b[0mev\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mevanselect\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpropselect\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvec_gen\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mord_schur\u001b[0m \u001b[1;33m=\u001b[0m\u001b[0;31m\\\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 583\u001b[1;33m \u001b[0munified_eigenproblem\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmatrices\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mtol\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 584\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 585\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mv\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m/home/maxtre/bin/anaconda/lib/python2.7/site-packages/kwant/physics/leads.pyc\u001b[0m in \u001b[0;36munified_eigenproblem\u001b[1;34m(a, b, tol)\u001b[0m\n\u001b[0;32m 374\u001b[0m \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 375\u001b[0m \u001b[0meps\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfinfo\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcommon_type\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0meps\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mtol\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 376\u001b[1;33m \u001b[0ms\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mt\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mz\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbeta\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mkla\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgen_schur\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcalc_q\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 377\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 378\u001b[0m \u001b[1;31m# Right-decaying modes.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m/home/maxtre/bin/anaconda/lib/python2.7/site-packages/kwant/linalg/decomp_schur.pyc\u001b[0m in \u001b[0;36mgen_schur\u001b[1;34m(a, b, calc_q, calc_z, calc_ev, overwrite_ab)\u001b[0m\n\u001b[0;32m 379\u001b[0m \u001b[0mgges\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlapack\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mltype\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m\"gges\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 380\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 381\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mgges\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcalc_q\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcalc_z\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcalc_ev\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 382\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 383\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32mkwant/linalg/lapack.pyx\u001b[0m in \u001b[0;36mkwant.linalg.lapack.zgges (kwant/linalg/lapack.c:28482)\u001b[1;34m()\u001b[0m\n",
"\u001b[1;31mLinAlgError\u001b[0m: QZ iteration failed to converge in zgges"
]
}
],
"source": [
"kwant.smatrix(rectangle_sys, 1.5).transmission(0, 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But it works on the lattice-periodic system"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"2.2074478672169042"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kwant.smatrix(lattice_sys, 1.5).transmission(0, 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Persists over large range:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"List all energies for which we get the QZ Error"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"energies = np.linspace(-5, 5, 100)\n",
"conductances = []\n",
"failures = []\n",
"for en in energies:\n",
" try:\n",
" conductances.append((en, kwant.smatrix(rectangle_sys, en).transmission(0, 1)))\n",
" except kwant.linalg.lapack.LinAlgError:\n",
" failures.append(en)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[-1.4646464646464645,\n",
" -1.3636363636363638,\n",
" -1.2626262626262625,\n",
" -1.1616161616161618,\n",
" -1.0606060606060606,\n",
" -0.95959595959595934,\n",
" -0.85858585858585901,\n",
" -0.75757575757575779,\n",
" -0.65656565656565657,\n",
" -0.55555555555555536,\n",
" -0.45454545454545503,\n",
" -0.35353535353535381,\n",
" -0.2525252525252526,\n",
" -0.15151515151515138,\n",
" -0.050505050505050164,\n",
" 0.050505050505050164,\n",
" 0.15151515151515138,\n",
" 0.2525252525252526,\n",
" 0.35353535353535381,\n",
" 0.45454545454545414,\n",
" 0.55555555555555536,\n",
" 0.65656565656565657,\n",
" 0.75757575757575779,\n",
" 0.85858585858585812,\n",
" 0.95959595959595934,\n",
" 1.0606060606060606,\n",
" 1.1616161616161618,\n",
" 1.2626262626262621,\n",
" 1.3636363636363633,\n",
" 1.4646464646464645,\n",
" 1.5656565656565657,\n",
" 1.666666666666667,\n",
" 1.7676767676767673,\n",
" 1.8686868686868685,\n",
" 1.9696969696969697,\n",
" 2.0707070707070709,\n",
" 2.1717171717171713,\n",
" 2.2727272727272725,\n",
" 2.3737373737373737,\n",
" 2.4747474747474749,\n",
" 2.5757575757575752,\n",
" 2.6767676767676765,\n",
" 2.7777777777777777,\n",
" 2.8787878787878789,\n",
" 2.9797979797979792,\n",
" 3.0808080808080813,\n",
" 3.1818181818181817,\n",
" 3.282828282828282,\n",
" 3.3838383838383841,\n",
" 3.4848484848484844,\n",
" 3.5858585858585865,\n",
" 3.6868686868686869,\n",
" 3.7878787878787872,\n",
" 3.8888888888888893,\n",
" 3.9898989898989896,\n",
" 4.0909090909090899,\n",
" 4.191919191919192,\n",
" 4.2929292929292924,\n",
" 4.3939393939393945,\n",
" 4.4949494949494948,\n",
" 4.5959595959595951,\n",
" 4.6969696969696972,\n",
" 4.7979797979797976,\n",
" 4.8989898989898997,\n",
" 5.0]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"failures"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[(-5.0, 0.0),\n",
" (-4.8989898989898988, 0.0),\n",
" (-4.7979797979797976, 0.0),\n",
" (-4.6969696969696972, 0.0),\n",
" (-4.595959595959596, 0.0),\n",
" (-4.4949494949494948, 0.0),\n",
" (-4.3939393939393936, 0.0),\n",
" (-4.2929292929292933, 0.0),\n",
" (-4.191919191919192, 0.0),\n",
" (-4.0909090909090908, 0.0),\n",
" (-3.9898989898989896, 0.0),\n",
" (-3.8888888888888888, 0.55007622553035029),\n",
" (-3.7878787878787881, 0.60532002089835035),\n",
" (-3.6868686868686869, 1.1607366729190312),\n",
" (-3.5858585858585856, 0.92724644062407424),\n",
" (-3.4848484848484849, 1.3571868690307214),\n",
" (-3.3838383838383841, 2.7535432149985439),\n",
" (-3.2828282828282829, 3.3011378020055369),\n",
" (-3.1818181818181817, 2.9184723900002503),\n",
" (-3.0808080808080809, 0.55372680080489989),\n",
" (-2.9797979797979797, 1.0444039180610929),\n",
" (-2.8787878787878789, 1.2345496926130244),\n",
" (-2.7777777777777777, 0.97824254804513178),\n",
" (-2.6767676767676769, 1.1751680631019943),\n",
" (-2.5757575757575757, 0.19384105607673346),\n",
" (-2.4747474747474749, 1.2874564707397094),\n",
" (-2.3737373737373737, 0.26279405116941068),\n",
" (-2.2727272727272729, 0.094029059607324175),\n",
" (-2.1717171717171717, 0.00458795629984937),\n",
" (-2.0707070707070709, 0.0014454478322902143),\n",
" (-1.9696969696969697, 0.0036447436870508205),\n",
" (-1.868686868686869, 0.0010561508098405376),\n",
" (-1.7676767676767677, 0.00040740066465199087),\n",
" (-1.6666666666666665, 0.0013185156055019946),\n",
" (-1.5656565656565657, 0.0068671498540652043)]"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"conductances"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
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"language_info": {
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"name": "python",
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