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Commit 0edb95b4 authored by Anton Akhmerov's avatar Anton Akhmerov Committed by Christoph Groth
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streamline test_selfenergy

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kwant/physics/selfenergy.py
+ 2
− 2
View file @ 0edb95b4
......@@ -548,7 +548,7 @@ def self_energy(h_onslice=None, h_hop=None, tol=1e6, lead_modes=None):
return la.solve(vecslmbdainv.T, vecs.T).T
def square_self_energy(width, hopping, potential, fermi_energy):
def square_self_energy(width, hopping, fermi_energy):
"""
Calculate analytically the self energy for a square lattice.
......@@ -584,7 +584,7 @@ def square_self_energy(width, hopping, potential, fermi_energy):
f_p = np.empty((width,), dtype=complex)
for p in xrange(width):
e = 2 * hopping * (1 - cos(factor * (p + 1)))
q = (fermi_energy - potential - e) / hopping - 2
q = (fermi_energy - e) / hopping - 2
f_p[p] = f(q)
# Put everything together into the self energy and return it.
......
kwant/physics/tests/test_selfenergy.py
+ 70
− 97
View file @ 0edb95b4
......@@ -11,49 +11,44 @@ import numpy as np
from numpy.testing import assert_almost_equal
import kwant.physics.selfenergy as se
def h_slice(t, w, e):
h = (4 * t - e) * np.identity(w)
h.flat[1 :: w + 1] = -t
h.flat[w :: w + 1] = -t
return h
def test_analytic_numeric():
w = 5 # width
t = 0.5 # hopping element
v = 2 # potential
e = 3.3 # Fermi energy
t = 0.78 # hopping element
e = 1.3 # Fermi energy
h_hop = -t * np.identity(w)
h_onslice = ((v + 4 * t - e)
* np.identity(w))
h_onslice.flat[1 :: w + 1] = -t
h_onslice.flat[w :: w + 1] = -t
assert_almost_equal(se.square_self_energy(w, t, e),
se.self_energy(h_slice(t, w, e), -t * np.identity(w)))
assert_almost_equal(se.square_self_energy(w, t, v, e),
se.self_energy(h_onslice, h_hop))
def test_regular_fully_degenerate():
"""This testcase features an invertible hopping matrix,
and bands that are fully degenerate.
"""Selfenergy with an invertible hopping matrix, and degenerate bands."""
This case can still be treated with the Schur technique."""
w = 2 # width
w = 6 # width
t = 0.5 # hopping element
v = 2 # potential
e = 3.3 # Fermi energy
e = 1.3 # Fermi energy
h_hop_s = -t * np.identity(w)
h_onslice_s = ((v + 4 * t - e)
* np.identity(w))
h_onslice_s.flat[1 :: w + 1] = -t
h_onslice_s.flat[w :: w + 1] = -t
h_onslice_s = h_slice(t, w, e)
h_hop = np.zeros((2*w, 2*w))
h_hop[0:w, 0:w] = h_hop_s
h_hop[w:2*w, w:2*w] = h_hop_s
h_hop[:w, :w] = h_hop_s
h_hop[w:, w:] = h_hop_s
h_onslice = np.zeros((2*w, 2*w))
h_onslice[0:w, 0:w] = h_onslice_s
h_onslice[w:2*w, w:2*w] = h_onslice_s
h_onslice[:w, :w] = h_onslice_s
h_onslice[w:, w:] = h_onslice_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[0:w, 0:w] = se.square_self_energy(w, t, v, e)
g[w:2*w, w:2*w] = se.square_self_energy(w, t, v, e)
g[:w, :w] = se.square_self_energy(w, t, e)
g[w:, w:] = se.square_self_energy(w, t, e)
assert_almost_equal(g, se.self_energy(h_onslice, h_hop))
......@@ -65,31 +60,27 @@ def test_regular_degenerate_with_crossing():
For this case the fall-back technique must be used.
"""
w = 2 # width
w = 4 # width
t = 0.5 # hopping element
v = 2 # potential
e = 3.3 # Fermi energy
e = 1.8 # Fermi energy
global h_hop
h_hop_s = -t * np.identity(w)
h_onslice_s = (v + 4 * t - e) * np.identity(w)
h_onslice_s.flat[1 :: w + 1] = -t
h_onslice_s.flat[w :: w + 1] = -t
h_onslice_s = h_slice(t, w, e)
h_hop = np.zeros((2*w, 2*w))
h_hop[0:w, 0:w] = h_hop_s
h_hop[w:2*w, w:2*w] = -h_hop_s
hop = np.zeros((2*w, 2*w))
hop[:w, :w] = h_hop_s
hop[w:, w:] = -h_hop_s
h_onslice = np.zeros((2*w, 2*w))
h_onslice[0:w, 0:w] = h_onslice_s
h_onslice[w:2*w, w:2*w] = -h_onslice_s
h_onslice[:w, :w] = h_onslice_s
h_onslice[w:, w:] = -h_onslice_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[0:w, 0:w] = se.square_self_energy(w, t, v, e)
g[w:2*w, w:2*w] = -np.conj(se.square_self_energy(w, t, v, e))
print np.round(g, 5)
print np.round(se.self_energy(h_onslice, h_hop), 5)
assert_almost_equal(g, se.self_energy(h_onslice, h_hop))
g[:w, :w] = se.square_self_energy(w, t, e)
g[w:, w:] = -np.conj(se.square_self_energy(w, t, e))
assert_almost_equal(g, se.self_energy(h_onslice, hop))
def test_singular():
"""This testcase features a rectangular (and hence singular)
......@@ -97,26 +88,22 @@ def test_singular():
This case can be treated with the Schur technique."""
w = 2 # width
w = 5 # width
t = .5 # hopping element
v = 0 # potential
e = 0 # Fermi energy
e = 0.4 # Fermi energy
h_hop_s = -t * np.identity(w)
h_onslice_s = ((v + 4 * t - e)
* np.identity(w))
h_onslice_s.flat[1 :: w + 1] = -t
h_onslice_s.flat[w :: w + 1] = -t
h_onslice_s = h_slice(t, w, e)
h_hop = np.zeros((2*w, w))
h_hop[w:2*w, 0:w] = h_hop_s
h_hop[w:, :w] = h_hop_s
h_onslice = np.zeros((2*w, 2*w))
h_onslice[0:w, 0:w] = h_onslice_s
h_onslice[0:w, w:2*w] = h_hop_s
h_onslice[w:2*w, 0:w] = h_hop_s
h_onslice[w:2*w, w:2*w] = h_onslice_s
g = se.square_self_energy(w, t, v, e)
h_onslice[:w, :w] = h_onslice_s
h_onslice[:w, w:] = h_hop_s
h_onslice[w:, :w] = h_hop_s
h_onslice[w:, w:] = h_onslice_s
g = se.square_self_energy(w, t, e)
print np.round(g, 5) / np.round(se.self_energy(h_onslice, h_hop), 5)
assert_almost_equal(g, se.self_energy(h_onslice, h_hop))
......@@ -128,28 +115,23 @@ def test_singular_but_square():
This case can be treated with the Schur technique."""
w = 5 # width
t = 0.5 # hopping element
v = 2 # potential
e = 3.3 # Fermi energy
t = 0.9 # hopping element
e = 2.38 # Fermi energy
h_hop_s = -t * np.identity(w)
h_onslice_s = ((v + 4 * t - e)
* np.identity(w))
h_onslice_s.flat[1 :: w + 1] = -t
h_onslice_s.flat[w :: w + 1] = -t
h_onslice_s = h_slice(t, w, e)
h_hop = np.zeros((2*w, 2*w))
h_hop[w:2*w, 0:w] = h_hop_s
h_hop[w:, :w] = h_hop_s
h_onslice = np.zeros((2*w, 2*w))
h_onslice[0:w, 0:w] = h_onslice_s
h_onslice[0:w, w:2*w] = h_hop_s
h_onslice[w:2*w, 0:w] = h_hop_s
h_onslice[w:2*w, w:2*w] = h_onslice_s
h_onslice[:w, :w] = h_onslice_s
h_onslice[:w, w:] = h_hop_s
h_onslice[w:, :w] = h_hop_s
h_onslice[w:, w:] = h_onslice_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[0:w, 0:w] = se.square_self_energy(w, t, v, e)
g[:w, :w] = se.square_self_energy(w, t, e)
assert_almost_equal(g, se.self_energy(h_onslice, h_hop))
def test_singular_fully_degenerate():
......@@ -159,36 +141,31 @@ def test_singular_fully_degenerate():
This case can still be treated with the Schur technique."""
w = 5 # width
t = 0.5 # hopping element
v = 2 # potential
t = 1.5 # hopping element
e = 3.3 # Fermi energy
h_hop_s = -t * np.identity(w)
h_onslice_s = ((v + 4 * t - e)
* np.identity(w))
h_onslice_s.flat[1 :: w + 1] = -t
h_onslice_s.flat[w :: w + 1] = -t
h_onslice_s = h_slice(t, w, e)
h_hop = np.zeros((4*w, 2*w))
h_hop[2*w:3*w, 0:w] = h_hop_s
h_hop[2*w:3*w, :w] = h_hop_s
h_hop[3*w:4*w, w:2*w] = h_hop_s
h_onslice = np.zeros((4*w, 4*w))
h_onslice[0:w, 0:w] = h_onslice_s
h_onslice[0:w, 2*w:3*w] = h_hop_s
h_onslice[:w, :w] = h_onslice_s
h_onslice[:w, 2*w:3*w] = h_hop_s
h_onslice[w:2*w, w:2*w] = h_onslice_s
h_onslice[w:2*w, 3*w:4*w] = h_hop_s
h_onslice[2*w:3*w, 0:w] = h_hop_s
h_onslice[2*w:3*w, :w] = h_hop_s
h_onslice[2*w:3*w, 2*w:3*w] = h_onslice_s
h_onslice[3*w:4*w, w:2*w] = h_hop_s
h_onslice[3*w:4*w, 3*w:4*w] = h_onslice_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[0:w, 0:w] = se.square_self_energy(w, t, v, e)
g[w:2*w, w:2*w] = se.square_self_energy(w, t, v, e)
g[:w, :w] = se.square_self_energy(w, t, e)
g[w:, w:] = se.square_self_energy(w, t, e)
assert_almost_equal(g,
se.self_energy(h_onslice, h_hop))
assert_almost_equal(g, se.self_energy(h_onslice, h_hop))
def test_singular_degenerate_with_crossing():
"""This testcase features a rectangular (and hence singular)
......@@ -198,33 +175,29 @@ def test_singular_degenerate_with_crossing():
This case must be treated with the fall-back technique."""
w = 5 # width
t = 0.5 # hopping element
v = 2 # potential
t = 20.5 # hopping element
e = 3.3 # Fermi energy
h_hop_s = -t * np.identity(w)
h_onslice_s = ((v + 4 * t - e)
* np.identity(w))
h_onslice_s.flat[1 :: w + 1] = -t
h_onslice_s.flat[w :: w + 1] = -t
h_onslice_s = h_slice(t, w, e)
h_hop = np.zeros((4*w, 2*w))
h_hop[2*w:3*w, 0:w] = h_hop_s
h_hop[2*w:3*w, :w] = h_hop_s
h_hop[3*w:4*w, w:2*w] = -h_hop_s
h_onslice = np.zeros((4*w, 4*w))
h_onslice[0:w, 0:w] = h_onslice_s
h_onslice[0:w, 2*w:3*w] = h_hop_s
h_onslice[:w, :w] = h_onslice_s
h_onslice[:w, 2*w:3*w] = h_hop_s
h_onslice[w:2*w, w:2*w] = -h_onslice_s
h_onslice[w:2*w, 3*w:4*w] = -h_hop_s
h_onslice[2*w:3*w, 0:w] = h_hop_s
h_onslice[2*w:3*w, :w] = h_hop_s
h_onslice[2*w:3*w, 2*w:3*w] = h_onslice_s
h_onslice[3*w:4*w, w:2*w] = -h_hop_s
h_onslice[3*w:4*w, 3*w:4*w] = -h_onslice_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[0:w, 0:w] = se.square_self_energy(w, t, v, e)
g[w:2*w, w:2*w] = -np.conj(se.square_self_energy(w, t, v, e))
g[:w, :w] = se.square_self_energy(w, t, e)
g[w:, w:] = -np.conj(se.square_self_energy(w, t, e))
assert_almost_equal(g,
se.self_energy(h_onslice, h_hop))
......
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