Small changes to Kane-Mele and Haldane examples

Author: greschd

examples/hm/haldane_model/haldane.py

@@ -16,10 +16,9 @@
 
 
 def Hamilton(k, m, t1, t2, phi):
-    k_a = 2 * np.pi / 3. * np.array([
-        -k[0] - k[1], 2. * k[0] - k[1], -k[0] + 2. * k[1]
-    ])
-    k_b = 2 * np.pi * np.array([k[0], -k[0] + k[1], k[1]])
+    kx, ky = k
+    k_a = 2 * np.pi / 3. * np.array([-kx - ky, 2. * kx - ky, -kx + 2. * ky])
+    k_b = 2 * np.pi * np.array([kx, -kx + ky, ky])
     H = 2 * t2 * np.cos(phi) * sum([np.cos(-val) for val in k_b]) * identity
     H += t1 * sum([np.cos(-val) for val in k_a]) * pauli_x
     H += t1 * sum([np.sin(-val) for val in k_a]) * pauli_y
@@ -30,13 +29,11 @@ def Hamilton(k, m, t1, t2, phi):
 
 def get_chern(m, t1, t2, phi):
     system = z2pack.hm.System(
-        lambda k: Hamilton(k, m, t1, t2, phi), bands=1, check_periodic=True
+        lambda k: Hamilton(k, m, t1, t2, phi), dim=2, bands=1
     )
 
     result = z2pack.surface.run(
-        system=system,
-        surface=lambda s, t: [t, s, 0.],
-        min_neighbour_dist=1e-5
+        system=system, surface=lambda s, t: [t, s], min_neighbour_dist=1e-5
     )
     return z2pack.invariant.chern(result)
 

examples/hm/kane_mele_model/run.py

@@ -20,7 +20,7 @@
 def get_kane_mele_hamiltonian(t, lambda_v, lambda_R, lambda_SO):
     def inner(k):
         k = np.array(k) * 2 * np.pi
-        kx, ky, kz = k
+        kx, ky = k
         # change to reduced coordinates
         x = (kx - ky) / 2
         y = (kx + ky) / 2
@@ -43,9 +43,10 @@ def inner(k):
         get_kane_mele_hamiltonian(
             t=1, lambda_v=0.1, lambda_R=0.05, lambda_SO=0.06
         ),
+        dim=2,
         check_periodic=True
     )
-    res = z2pack.surface.run(system=system, surface=lambda s, t: [s / 2, t, 0])
+    res = z2pack.surface.run(system=system, surface=lambda s, t: [s / 2, t])
     print('Z2 invariant: {}'.format(z2pack.invariant.z2(res)))
     fig, ax = plt.subplots(figsize=[5, 3])
     z2pack.plot.wcc(res, axis=ax)

tests/test_hm.py

@@ -37,6 +37,23 @@ def test_explicit_bands(bands, weyl_surface, compare_wcc):
     compare_wcc(res.wcc)
 
 
+def test_non_periodic_raises():
+    """
+    Test that the check for periodicity of Hamiltonians raises when given a
+    non-periodic value.
+    """
+    with pytest.raises(ValueError):
+        system = z2pack.hm.System(  # pylint: disable=unused-variable
+            lambda k: np.array(
+                [
+                    [k[2], k[0] -1j * k[1]],
+                    [k[0] + 1j * k[1], -k[2]]
+                ]
+            ),
+            check_periodic=True
+        )
+
+
 def test_invalid_pos():
     """
     Test that trying to set too many positions raises.

z2pack/hm.py

@@ -37,7 +37,7 @@ class System(EigenstateSystem):
     :param convention: The convention used for the Hamiltonian, following the `pythtb formalism <http://www.physics.rutgers.edu/pythtb/_downloads/pythtb-formalism.pdf>`_. Convention 1 means that the eigenvalues of :math:`\mathcal{H}(\mathbf{k})` are wave vectors :math:`\left|\psi_{n\mathbf{k}}\right>`. With convention 2, they are the cell-periodic Bloch functions :math:`\left|u_{n\mathbf{k}}\right>`.
     :type convention: int
 
-    :param check_periodic: Evaluate the Hamiltonian at :math:`\{0, 1\}^d` as a simple check if it is periodic.
+    :param check_periodic: Evaluate the Hamiltonian at :math:`\{0, 1\}^d` as a simple check if it is periodic. Note that this does not work if the Hamiltonian is written such that the eigenstates acquire a phase when being translated by a lattice vector.
     :type check_periodic: bool
     """
 
@@ -63,12 +63,13 @@ def __init__(
 
         if check_periodic:
             k_values = itertools.product([0, 1], repeat=dim)
-            ham_gamma = self._hamilton(next(k_values))
+            k_first = next(k_values)
+            ham_first = self._hamilton()
             for k in k_values:
-                if not np.allclose(ham_gamma, self._hamilton(k)):
+                if not np.allclose(ham_first, self._hamilton(k)):
                     raise ValueError(
-                        'The given Hamiltonian is not periodic: H(k=0) != H(k={})'
-                        .format(k)
+                        'The given Hamiltonian is not periodic: H(k={}) != H(k={})'
+                        .format(k_first, k)
                     )
 
         size = len(self._hamilton([0] * dim))  # assuming to be square...