Add optional test for periodicity of Hamiltonian

Author: greschd

examples/hm/haldane_model/haldane.py

@@ -29,7 +29,9 @@ 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)
+    system = z2pack.hm.System(
+        lambda k: Hamilton(k, m, t1, t2, phi), bands=1, check_periodic=True
+    )
 
     result = z2pack.surface.run(
         system=system,

examples/hm/kane_mele_model/run.py

@@ -16,6 +16,7 @@
 pauli_y = np.array([[0, -1j], [1j, 0]], dtype=complex)
 pauli_z = np.array([[1, 0], [0, -1]], dtype=complex)
 
+
 def get_kane_mele_hamiltonian(t, lambda_v, lambda_R, lambda_SO):
     def inner(k):
         k = np.array(k) * 2 * np.pi
@@ -28,18 +29,21 @@ def inner(k):
             lambda_v * kron(pauli_z, identity) +
             lambda_R * (1 - cos(x) * cos(y)) * kron(pauli_y, pauli_x) +
             -sqrt(3) * lambda_R * sin(x) * sin(y) * kron(pauli_y, pauli_y) +
-            2 * t * cos(x) * sin(y) * kron(pauli_y, identity) +
-            lambda_SO * (2 * sin(2 * x) - 4 * sin(x) * cos(y)) * kron(pauli_z, pauli_z) +
+            2 * t * cos(x) * sin(y) * kron(pauli_y, identity) + lambda_SO *
+            (2 * sin(2 * x) - 4 * sin(x) * cos(y)) * kron(pauli_z, pauli_z) +
             lambda_R * cos(x) * sin(y) * kron(pauli_x, pauli_x) +
             -sqrt(3) * lambda_R * sin(x) * cos(y) * kron(pauli_x, pauli_y)
         )
+
     return inner
 
+
 if __name__ == '__main__':
     system = z2pack.hm.System(
         get_kane_mele_hamiltonian(
             t=1, lambda_v=0.1, lambda_R=0.05, lambda_SO=0.06
-        )
+        ),
+        check_periodic=True
     )
     res = z2pack.surface.run(system=system, surface=lambda s, t: [s / 2, t, 0])
     print('Z2 invariant: {}'.format(z2pack.invariant.z2(res)))

z2pack/hm.py

@@ -4,6 +4,8 @@
 This module contains a class for creating Systems which are described by a Hamiltonian matrix (hm), such as k•p models.
 """
 
+import itertools
+
 import numpy as np
 import scipy.linalg as la
 from fsc.export import export
@@ -34,6 +36,9 @@ 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.
+    :type check_periodic: bool
     """
 
     def __init__(
@@ -44,7 +49,8 @@ def __init__(
         pos=None,
         bands=None,
         hermitian_tol=1e-6,
-        convention=2
+        convention=2,
+        check_periodic=False
     ):
         self._hamilton = hamilton
         self._hermitian_tol = hermitian_tol
@@ -55,6 +61,16 @@ def __init__(
                 format(self._convention)
             )
 
+        if check_periodic:
+            k_values = itertools.product([0, 1], repeat=dim)
+            ham_gamma = self._hamilton(next(k_values))
+            for k in k_values:
+                if not np.allclose(ham_gamma, self._hamilton(k)):
+                    raise ValueError(
+                        'The given Hamiltonian is not periodic: H(k=0) != H(k={})'
+                        .format(k)
+                    )
+
         size = len(self._hamilton([0] * dim))  # assuming to be square...
         # add one atom for each orbital in the hamiltonian
         if pos is None: