def __init__(self):
points = np.array([
[0.0, 0.0],
[1.0, 0.0],
[2.0, 0.0],
[3.0, 0.0],
[4.0, 0.0],
[5.0, 0.0],
[0.5, np.sqrt(3) / 2],
[1.5, np.sqrt(3) / 2],
[2.5, np.sqrt(3) / 2],
[3.5, np.sqrt(3) / 2],
[4.5, np.sqrt(3) / 2],
[5.5, np.sqrt(3) / 2],
],
dtype=np.float64)
vectors = np.array([[6.0, 0.0], [3.0, np.sqrt(3)]], dtype=np.float64)
cluster = Lattice(points, vectors)
intra, inter = cluster.bonds(nth=1)
x_bonds = []
y_bonds = []
z_bonds = []
for bond in intra + inter:
p0, p1 = bond.endpoints
index0 = cluster.getIndex(site=p0, fold=True)
index1 = cluster.getIndex(site=p1, fold=True)
bond_index = (index0, index1)
azimuth = bond.getAzimuth(ndigits=0)
if azimuth in (-180, 0, 180):
x_bonds.append(bond_index)
elif azimuth in (-120, 60):
z_bonds.append(bond_index)
elif azimuth in (-60, 120):
y_bonds.append(bond_index)
else:
raise RuntimeError("Invalid bond azimuth: {0}".format(azimuth))
self._identity = "Triangle12"
self._cluster = cluster
self._x_bonds = tuple(x_bonds)
self._y_bonds = tuple(y_bonds)
self._z_bonds = tuple(z_bonds)
import matplotlib.pyplot as plt
import numpy as np
from HamiltonianPy import KPath, Lattice
SQRT3 = np.sqrt(3)
POINTS = np.array(
[[0.0, 0.0], [1.0, SQRT3], [2.0, 0.0], [3.0, SQRT3], [1.0, 1.0 / SQRT3]],
dtype=np.float64)
VECTORS = np.array([[4.0, 0.0], [2.0, 2 * SQRT3]], dtype=np.float64)
t0 = 0.0
t1 = -1.00
t2 = -0.25
id = "t0={0:.2f}_t1={1:.2f}_t2={2:.2f}".format(t0, t1, t2)
cluster = Lattice(POINTS, VECTORS)
intra_bonds_1st, inter_bonds_1st = cluster.bonds(nth=1)
intra_bonds_2nd, inter_bonds_2nd = cluster.bonds(nth=2)
intra_bonds_6th, inter_bonds_6th = cluster.bonds(nth=6)
HTerms = []
for bond in intra_bonds_1st + inter_bonds_1st:
p0, p1 = bond.endpoints
p0_eqv, dR0 = cluster.decompose(p0)
p1_eqv, dR1 = cluster.decompose(p1)
index0 = cluster.getIndex(p0_eqv)
index1 = cluster.getIndex(p1_eqv)
HTerms.append((index0, index1, t0, dR0 - dR1))
for bond in intra_bonds_2nd + inter_bonds_2nd:
p0, p1 = bond.endpoints
p0_eqv, dR0 = cluster.decompose(p0)
def __init__(self, num1=4, num2=6, direction="xy"):
"""
On triangular lattice, the nearest-neighbor (NN) bonds along the
zero-degree direction is defined as the x-type bond (x-bond); NN bonds
along the 120-degree direction is defined as the y-type bond (y-bond);
NN bonds along the 60-degree direction is defined as the z-type bond
(z-bond). The definition of the x, y, z bond is counterclockwise.
Parameters
----------
num1, num2 : int, optional
The number of lattice site along the 1st and 2nd translation vector.
The default values for `num1` and `num2` are 4 and 6 respectively.
direction : ["xy" | "xz" | "yx" | "yz" | "zx" | "zy"], optional
Define the direction of the cluster. This parameter determine the
interpretation of the `num1` and `num2` parameters. For example,
if `direction` is set to "xy", then there are `num1` lattice sites
along the x-bond direction and `num2` lattice sites along the
y-bond direction.
Default: "xy".
"""
assert isinstance(num1, int) and num1 > 0
assert isinstance(num2, int) and num2 > 0
assert direction in ("xy", "xz", "yx", "yz", "zx", "zy")
identity = "num1={0}_num2={1}_direction={2}".format(
num1, num2, direction
)
RX = np.array([1.0, 0.0], dtype=np.float64)
RY = np.array([-0.5, np.sqrt(3) / 2], dtype=np.float64)
RZ = np.array([0.5, np.sqrt(3) / 2], dtype=np.float64)
AS = {
"xy": np.array([RX, RY], dtype=np.float64),
"xz": np.array([RX, RZ], dtype=np.float64),
"yx": np.array([RY, RX], dtype=np.float64),
"yz": np.array([RY, RZ], dtype=np.float64),
"zx": np.array([RZ, RX], dtype=np.float64),
"zy": np.array([RZ, RY], dtype=np.float64),
}
As = AS[direction]
vectors = As * np.array([[num1], [num2]])
points = np.dot([[i, j] for i in range(num1) for j in range(num2)], As)
cluster = Lattice(points=points, vectors=vectors, name=identity)
intra, inter = cluster.bonds(nth=1)
x_bonds = []
y_bonds = []
z_bonds = []
for bond in intra + inter:
p0, p1 = bond.endpoints
index0 = cluster.getIndex(site=p0, fold=True)
index1 = cluster.getIndex(site=p1, fold=True)
bond_index = (index0, index1)
azimuth = bond.getAzimuth(ndigits=0)
# The definition of x, y, z bond in a trio is counterclockwise.
if azimuth in (-180, 0, 180):
x_bonds.append(bond_index)
elif azimuth in (-120, 60):
z_bonds.append(bond_index)
elif azimuth in (-60, 120):
y_bonds.append(bond_index)
else:
raise RuntimeError("Invalid bond azimuth: {0}".format(azimuth))
self._num1 = num1
self._num2 = num2
self._direction = direction
self._identity = identity
self._cluster = cluster
self._x_bonds = tuple(x_bonds)
self._y_bonds = tuple(y_bonds)
self._z_bonds = tuple(z_bonds)
import matplotlib.pyplot as plt
import numpy as np
from HamiltonianPy import Lattice
from database import POINTS, VECTORS
cluster_points = np.append(POINTS, [[0.0, 0.0]], axis=0)
cluster = Lattice(cluster_points, VECTORS)
intra_bonds_1st, inter_bonds_1st = cluster.bonds(nth=1)
intra_bonds_3rd, inter_bonds_3rd = cluster.bonds(nth=3)
fig, ax = plt.subplots()
for point in cluster_points:
cluster_index = cluster.getIndex(point, fold=True)
if cluster_index == 12:
color = "tab:red"
marker_size = 25
else:
color = "black"
marker_size = 20
ax.plot(point[0],
point[1],
marker="o",
ms=marker_size,
color=color,
zorder=2)
ax.text(point[0],
point[1] - 0.2,
str(cluster_index),
ha="center",
va="top",
[0.5, 0.5 * SQRT3],
[1.5, 0.5 * SQRT3],
[2.5, 0.5 * SQRT3],
[3.5, 0.5 * SQRT3],
[1.0, SQRT3],
[2.0, SQRT3],
[3.0, SQRT3],
[4.0, SQRT3],
[1.5, 1.5 * SQRT3],
[2.5, 1.5 * SQRT3],
[3.5, 1.5 * SQRT3],
[4.5, 1.5 * SQRT3],
],
dtype=np.float64)
CLUSTER = Lattice(POINTS, np.array([[4.0, 0.0], [2.0, 2 * SQRT3]]))
INTRA_BONDS, INTER_BONDS = CLUSTER.bonds(nth=1)
_SPIN_UP = [-1, 1, 1]
_SPIN_DOWN = [1, -1, -1]
VECTORS0 = np.array([
_SPIN_UP,
_SPIN_UP,
_SPIN_UP,
_SPIN_UP,
_SPIN_DOWN,
_SPIN_DOWN,
_SPIN_DOWN,
_SPIN_DOWN,
_SPIN_UP,
_SPIN_UP,
_SPIN_UP,
