PyTB 1.5

Original v1.5 release from http://www.physics.rutgers.edu/~dhv/pytb/

INSTALL

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+In order to install PyTB package, simply execute this command as root
+
+  python setup.py install
+
+or execute this command as normal (non-root) user 
+
+  sudo python setup.py install
+
+If you do not have root privileges then you can use the following command
+to install PyTB in arbitrary folder DIR
+
+  python setup.py install --home=DIR
+
+After executing this command you will need to add "DIR/lib/python" or equivalent
+to PYTHONPATH variable. For example, in bash you would use
+
+  export PYTHONPATH=$PYTHONPATH:DIR/lib/python
+
+
+For more details on PyTB package go to
+
+http://www.physics.rutgers.edu/~dhv/pytb

PKG-INFO

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+Metadata-Version: 1.0
+Name: pytb
+Version: 1.5
+Summary: Simple solver for tight binding models.
+Home-page: http://www.physics.rutgers.edu/~dhv/pytb
+Author: Sinisa Coh and David Vanderbilt
+Author-email: [email protected]  [email protected]
+License: gpl-3.0
+Description: The tight binding method is an approximate
+        approach for solving for the electronic wave functions for
+        electrons in solids assuming a basis of localized atomic-like
+        orbitals.
+Platform: UNIX
+Platform: Windows
+Platform: Mac OS X

examples/0dim.py

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+#!/usr/bin/env python
+
+# Version 1.5
+# zero dimensional tight-binding model of a NH3 molecule
+
+# Copyright under GNU General Public License 2010, 2012
+# by Sinisa Coh and David Vanderbilt (see gpl-pytb.txt)
+
+from pytb import * # import TB model class
+import numpy as nu
+import pylab as pl
+
+# define lattice vectors
+lat=[[1.0,0.0,0.0],[0.0,1.0,0.0],[0.0,0.0,1.0]]
+# define coordinates of orbitals
+sq32=nu.sqrt(3.0)/2.0
+orb=[[(2./3.)*sq32,0.,0.],
+     [(-1./3.)*sq32,1./2.,0.],
+     [(-1./3.)*sq32,-1./2.,0.],
+     [0.,0.,1.]]
+# make zero dimensional tight-binding model
+my_model=tbmodel(0,3,lat,orb)
+
+# set model parameters
+delta=0.5
+t_first=1.0
+
+# change on-site energies so that N and H don't have the same energy
+my_model.set_sites([-delta,-delta,-delta,delta])
+# set hoppings (one for each connected pair of orbitals)
+# (amplitude, i, j)
+my_model.add_hop(t_first, 0, 1)
+my_model.add_hop(t_first, 0, 2)
+my_model.add_hop(t_first, 0, 3)
+my_model.add_hop(t_first, 1, 2)
+my_model.add_hop(t_first, 1, 3)
+my_model.add_hop(t_first, 2, 3)
+
+# print tight-binding model
+my_model.display()
+
+print '---------------------------------------'
+print 'starting calculation'
+print '---------------------------------------'
+print 'Calculating bands...'
+print
+print 'Band energies'
+print    
+# solve for eigenenergies of hamiltonian
+evals=my_model.solve_all()
+
+# First make a figure object
+fig=pl.figure()
+# plot all states
+pl.plot(evals,"bo")
+pl.ylim(-1.8,3.2)
+pl.xlim(-1.,4.)
+# put title
+pl.title("Molecule levels")
+# make an PDF figure of a plot
+pl.savefig("spectrum.pdf")                    
+
+print 'Done.\n'

examples/checkerboard.py

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+#!/usr/bin/env python
+
+# Version 1.5
+# two dimensional tight-binding checkerboard model
+
+# Copyright under GNU General Public License 2010, 2012
+# by Sinisa Coh and David Vanderbilt (see gpl-pytb.txt)
+
+from pytb import * # import TB model class
+import numpy as nu
+import pylab as pl
+
+# define lattice vectors
+lat=[[1.0,0.0],[0.0,1.0]]
+# define coordinates of orbitals
+orb=[[0.0,0.0],[0.5,0.5]]
+
+# make two dimensional tight-binding checkerboard model
+my_model=tbmodel(2,2,lat,orb)
+
+# set model parameters
+delta=1.1
+t=0.6
+
+# set on-site energies
+my_model.set_sites([-delta,delta])
+# set hoppings (one for each connected pair of orbitals)
+# (amplitude, i, j, [lattice vector to cell containing j])
+my_model.add_hop(t, 1, 0, [0, 0])
+my_model.add_hop(t, 1, 0, [1, 0])
+my_model.add_hop(t, 1, 0, [0, 1])
+my_model.add_hop(t, 1, 0, [1, 1])
+
+# print tight-binding model
+my_model.display()
+
+# generate list of k-points following some high-symmetry line in
+# the k-space. Variable kpts here is just an array of k-points
+path=[[0.0,0.0],[0.0,0.5],[0.5,0.5],[0.0,0.0]]
+kpts=k_path(path,100)
+print '---------------------------------------'
+print 'report of k-point path'
+print '---------------------------------------'
+print 'Path runs over',len(kpts),'k-points connecting:'
+for k in path:
+    print k
+print
+
+print '---------------------------------------'
+print 'starting calculation'
+print '---------------------------------------'
+print 'Calculating bands...'
+
+# solve for eigenenergies of hamiltonian on
+# the set of k-points from above
+evals=my_model.solve_all(kpts)
+
+# plotting of band structure
+print 'Plotting bandstructure...'
+
+# First make a figure object
+fig=pl.figure()
+# plot first band
+pl.plot(evals[0])
+# plot second band
+pl.plot(evals[1])
+# put title
+pl.title("Checkerboard band structure")
+# make an PDF figure of a plot
+pl.savefig("band.pdf")
+
+print 'Done.\n'

examples/eigenvector.py

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+#!/usr/bin/env python
+
+# Version 1.5
+# prints out eigenvectors of two dimensional tight-binding checkerboard model
+
+# Copyright under GNU General Public License 2010, 2012
+# by Sinisa Coh and David Vanderbilt (see gpl-pytb.txt)
+
+from pytb import * # import TB model class
+import numpy as nu
+import pylab as pl
+
+# define lattice vectors
+lat=[[1.0,0.0],[0.0,1.0]]
+# define coordinates of orbitals
+orb=[[0.0,0.0],[0.5,0.5]]
+
+# make two dimensional tight-binding checkerboard model
+my_model=tbmodel(2,2,lat,orb)
+
+# set model parameters
+delta=1.1
+t=0.6
+
+# set on-site energies
+my_model.set_sites([-delta,delta])
+# set hoppings (one for each connected pair of orbitals)
+# (amplitude, i, j, [lattice vector to cell containing j])
+my_model.add_hop(t, 1, 0, [0, 0])
+my_model.add_hop(t, 1, 0, [1, 0])
+my_model.add_hop(t, 1, 0, [0, 1])
+my_model.add_hop(t, 1, 0, [1, 1])
+
+# print tight-binding model
+my_model.display()
+
+# generate list of k-points following some high-symmetry line in
+# the k-space. Variable kpts here is just an array of k-points
+path=[[0.0,0.0],[0.0,0.5]]
+kpts=k_path(path,10)
+print '---------------------------------------'
+print 'report of k-point path'
+print '---------------------------------------'
+print 'Path runs over',len(kpts),'k-points connecting:'
+for k in path:
+    print k
+print
+
+print '---------------------------------------'
+print 'starting calculation'
+print '---------------------------------------'
+print 'Calculating bands...'
+
+# solve for eigenenergies of hamiltonian on
+# the set of k-points from above
+(evals,evects)=my_model.solve_all(kpts,eig_vectors=True)
+
+print 'Print out eigenvalues and eigenvectors'
+
+# go over all k-points
+for k in range(len(kpts)):
+    print 'k-vector --> ',kpts[k]
+      # go over all bands
+    for b in range(2):
+        print ' band --> ', b
+        print ' eigenvalue --> ',evals[b,k]
+        # go over all sites
+        for s in range(2):
+            print '  u_nk(orbital='+str(s)+') --> ',
+            print evects[b,k,s]
+
+# First make a figure object
+fig=pl.figure()
+# plot real part of the wavefunction of first band at second orbital
+pl.plot(evects[0,:,1].real)
+pl.ylim(-1.,1.)
+# put title
+pl.title("Real part of the wf. of 1st band at 2nd orbital")
+# make an PDF figure of a plot
+pl.savefig("evec.pdf")
+
+print 'Done.\n'