Debugging non-Bravais Lattice TBLattice

[andrewkhardy]

I'd like to check something with RPA on the honeycomb lattice, but I am unable to get the TBLattice object in TRIQS to give me a honeycomb dispersion. I am not asking for anyone to debug my code, but if anyone has suggestions for how to determine what is going wrong, I'd appreciate it.

Code supplied: (pulling things out of a class so easier to read)

params = {'t' : 1, 'n_k': 30, 'n_orbs' :1}
gf_struct = []
 s_z = np.array([[1,0],[0,-1]])
 id = np.eye(2*params["n_orbs"])
 s_x = np.array([[0,1],[1,0]])
 hopp = np.kron(s_x,id) 
 for o in range(0, params["n_orbs"]):
     gf_struct.append("up_c-" + str(o))
     gf_struct.append("dn_c-" + str(o))
     gf_struct.append("up_f-" + str(o))
     gf_struct.append("dn_f-" + str(o))
 H = TBLattice(
 units = [(3/2, np.sqrt(3)/2, 0.0), (3/2, -np.sqrt(3)/2, 0.0)],
 hopping = {
     # nearest neighbour hopping -params["t"]
     ( +1/3,-1/3): -params["t"] * hopp,
     ( -1/3,+1/3): -params["t"] * hopp,
     ( -2/3,-1/3): -params["t"] * hopp,
     ( +2/3,+1/3): -params["t"] * hopp,
     ( -1/3,-2/3): -params["t"] * hopp,
     ( +1/3,+2/3): -params["t"] * hopp,
     },
 orbital_positions = [(0,0,0),(0,0,0), (1,0,0),(1,0,0)]*params["n_orbs"],
 orbital_names = gf_struct,
 )
G = np.array([0.0, 0.0, 0.0])
M1 = np.array([0.5, 0.0, 0.0])
K2 = np.array([2/3, 1/3, 0.0])
paths = [(G, M1), (M1, K2), (K2, G)]
k_vecs, k_plot, k_ticks = k_space_path(paths, bz=H.bz)
kmesh = H.get_kmesh(n_k=(params["n_k"],params["n_k"], 1))
e_k = H.fourier(kmesh)
bandstructure = np.array([np.linalg.eigvals(e_k(k)) for k in k_vecs])
bands_plot = plt.plot(k_plot, bandstructure[:,0])
bands_plot = plt.plot(k_plot, bandstructure[:,2])

These flat energies are not the honeycomb band structure. I am now trying to debug.
My question is that I have no manner of seeing if the bonds are actually going from the "c" to "f" sites, (A,B sublattice) or not. The documentation always mentions Bravais lattices, are non-Bravais lattices not supported? Are there ways to plot real-space bonds or the real-space Hamiltonian to see if sites are being connected or if not, what is wrong?

[andrewkhardy]

params = {'t' : 1, 'n_k': 30, 'n_orbs' :1}
gf_struct = []
s_z = np.array([[1,0],[0,-1]])
id = np.eye(2*params["n_orbs"])
s_x = np.array([[0,1],[1,0]])

s_x_1 = np.array([[0,1],[0,0]])
s_x_2 = np.array([[0,0],[1,0]])
hopp = np.kron(s_x,id)
hopp_1 = np.kron(s_x_1,id) 
hopp_2 = np.kron(s_x_2,id) 

for o in range(0, params["n_orbs"]):
    gf_struct.append("up_c-" + str(o))
    gf_struct.append("up_f-" + str(o))
    gf_struct.append("dn_c-" + str(o))
    gf_struct.append("dn_f-" + str(o))

H = TBLattice(
units = [(1/2, np.sqrt(3)/2, 0.0), (1/2, -np.sqrt(3)/2, 0.0)],


hopping = {
    # nearest neighbour hopping -params["t"]
    ( 0,0): -params["t"] * hopp,
    ( 0,-1): -params["t"] * hopp_1,
    ( 0,+1): -params["t"] * hopp_2,
    ( -1,0): -params["t"] * hopp_1,
    ( +1,0): -params["t"] * hopp_2,
    },
orbital_positions = [(0,0,0),(0,0,0), (0,1/np.sqrt(3),0),(0,1/np.sqrt(3),0)]*params["n_orbs"],
orbital_names = gf_struct,
)
G = np.array([0.0, 0.0, 0.0])
M1 = np.array([0.5, 0.0, 0.0])
K2 = np.array([2/3, 1/3, 0.0])
paths = [(G, M1), (M1, K2), (K2, G)]
#H = H_triangle(params).H
k_vecs, k_plot, k_ticks = k_space_path(paths, bz=H.bz)
kmesh = H.get_kmesh(n_k=(parms["n_k"],parms["n_k"], 1))
e_k = H.fourier(kmesh)
bandstructure = np.array([np.linalg.eigvals(e_k(k)) for k in k_vecs])
bands_plot = plt.plot(k_plot, bandstructure[:,0])
bands_plot = plt.plot(k_plot, bandstructure[:,1])

If anyone else gets stuck on a similar issue, here is the corrected form, the displacement vectors need to be to unit cells and not sites.