import numpy as np
import matplotlib.pyplot as plt
 
# Define the parameters
t = 1.0  # Hopping amplitude
N = 50   # Number of lattice sites
phi = np.pi / 4  # Phase factor (example: pi/4)
 
# Generate the mode indices (1 to N)
n = np.arange(1, N+1)
 
# Calculate the energy dispersion for each mode n
epsilon_n = -4 * t * np.cos(n * np.pi / (N+1)) * np.cos(phi)
 
# Plot the energy dispersion
plt.figure(figsize=(8, 6))
plt.plot(n, epsilon_n, label=r'$\epsilon_n = -4t \cos(\frac{n\pi}{N+1}) \cos(\phi)$')
plt.title("Energy Dispersion in Tight-Binding Chain with Peierls Substitution")
plt.xlabel("Mode index (n)")
plt.ylabel("Energy ($\epsilon_n$)")
plt.grid(True)
plt.legend()
plt.show()
 

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