Merge pull request #20 from Imperial-CMTH/chern_number

Chern number

Author: dpreuo

src/koala/chern_number.py

@@ -0,0 +1,45 @@
+from koala.lattice import Lattice
+import numpy as np
+import scipy.linalg as la
+
+def crosshair_marker(lattice: Lattice, projector: np.ndarray, crosshair_position: np.ndarray):
+    """Generate the crosshair marker for a lattice and Hamiltonian
+
+    :param lattice: the lattice on which the Hamiltonian is placed 
+    :type lattice: Lattice
+    :param projector: A projectro onto a set of occupied states
+    :type projector: np.ndarray
+    :param crosshair_position: the position of the crosshair in the bulk
+    :type crosshair_position: np.ndarray
+    :return: an array giving the marker value at every point in the system
+    :rtype: np.ndarray
+    """
+
+
+    positions = lattice.vertices.positions
+    theta_x_vec = np.diag(1*(positions[:,0] < crosshair_position[0]))
+    theta_y_vec = np.diag(1*(positions[:,1] < crosshair_position[1]))
+
+    crosshair_marker = 4*np.pi*np.diag(projector@theta_x_vec@projector@theta_y_vec@projector).imag
+
+    return crosshair_marker
+
+
+def chern_marker(lattice: Lattice, projector: np.ndarray):
+    """generate the Chern marker for the system
+
+    :param lattice: the lattice 
+    :type lattice: Lattice
+    :param projector: a projector onto a set of occupied states
+    :type projector: np.ndarray
+    :return: the Chern marker value for each point in the system
+    :rtype: np.ndarray
+    """
+
+    positions = lattice.vertices.positions
+    X = np.diag(positions[:,0])
+    Y = np.diag(positions[:,1])
+
+    chern_marker = 4*np.pi*np.diag(projector@X@projector@Y@projector).imag
+
+    return chern_marker

tests/test_chern_number.py

@@ -0,0 +1,32 @@
+from koala.pointsets import generate_random
+from koala.voronization import generate_lattice
+from koala.graph_color import color_lattice
+from koala.hamiltonian import generate_majorana_hamiltonian
+from numpy import linalg as la
+import numpy as np
+import matplotlib
+from koala import chern_number as cn
+
+def test_chern_and_crosshair():
+    # define the lattice system
+    number_of_plaquettes = 50
+    points = generate_random(number_of_plaquettes)
+    lattice = generate_lattice(points)
+
+    # color the lattice
+    coloring = color_lattice(lattice)
+
+    # parameters
+    ujk = np.full(lattice.n_edges, 1)
+    J = np.array([1,1,1])
+
+    # solve system
+    H_maj = generate_majorana_hamiltonian(lattice, coloring, ujk, J)
+    eigs, vecs = la.eigh (H_maj)
+    lowest_diag = np.array([1]*(lattice.n_vertices//2) + [0]*(lattice.n_vertices//2) )
+    P = vecs @ np.diag(lowest_diag) @ vecs.conj().T
+
+    # find crosshair / chern number
+    crosshair_position = np.array([0.5,0.5])
+    crosshair_marker = cn.crosshair_marker(lattice, P, crosshair_position)
+    chern_marker = cn.chern_marker(lattice, P)