Isotropic spin-spin correlator for 1D J1–J2 model with PBC

[aruneel]

I am a new member of TenPy. I have been trying to compute the istropic spin-spin correlation \(C(r) = \frac{1}{L}\sum_{i=1}^{L} (S^{x}_{i}S^{x}_{i+r}+S^{y}_{i}S^{y}_{i+r}+S^{z}_{i}S^{z}_{i+r}) \) using TenPy for the antiferromagnetic 1D \(J1-J2\) model with PBC for \(L = 20\) and check it against the exact diagonalization. The code I have written is given below.

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# --- Imports ---
import numpy as np
import matplotlib.pyplot as plt
from tenpy.models.model import CouplingMPOModel
from tenpy.networks.site import SpinHalfSite
from tenpy.models.lattice import Chain
from tenpy.networks.mps import MPS
from tenpy.algorithms import dmrg

# --- Custom J1–J2 Heisenberg Model ---
class J1J2Model(CouplingMPOModel):
    def init_sites(self, model_params):
        conserve = model_params.get('conserve', None)
        return SpinHalfSite(conserve=conserve)

    def init_terms(self, model_params):
        J1 = model_params.get('J1', 1.0)
        J2 = model_params.get('J2', 0.0)

        for u1, u2, dx in self.lat.pairs['nearest_neighbors']:
            self.add_coupling(J1, u1, 'Sz', u2, 'Sz', dx)
            self.add_coupling(0.5 * J1, u1, 'Sp', u2, 'Sm', dx, plus_hc=True)

        for u1, u2, dx in self.lat.pairs['next_nearest_neighbors']:
            self.add_coupling(J2, u1, 'Sz', u2, 'Sz', dx)
            self.add_coupling(0.5 * J2, u1, 'Sp', u2, 'Sm', dx, plus_hc=True)

# --- Parameters ---
L = 20
J1 = 1.0
J2 = 0.0

# --- Lattice with PBC ---
lat = Chain(L, site=SpinHalfSite(conserve=None), bc='periodic')

# --- Model ---
model_params = {'lattice': lat, 'J1': J1, 'J2': J2}
model = J1J2Model(model_params)

# --- Initial MPS ---
init_state = ['up', 'down'] * (L // 2)
psi = MPS.from_product_state(model.lat.mps_sites(), init_state, bc='finite')

# --- Run DMRG ---
dmrg_params = {
    'mixer': True,
    'max_E_err': 1e-10,
    'trunc_params': {'chi_max': 800, 'svd_min': 1e-10},
    'max_sweeps': 20,
}
info = dmrg.run(psi, model, dmrg_params)

# --- Print and rescale energy ---
E_tp = info['E']
E_tp_scaled = 4.0*E_tp   # match NetKet convention
print(f"Ground state energy (TeNPy):        {E_tp:.12f}")
print(f"Rescaled energy to match NetKet ED: {E_tp_scaled:.12f}")


# --- Site-local spin operators ---
Sx = [model.lat.mps_sites()[i].Sx for i in range(L)]
Sy = [model.lat.mps_sites()[i].Sy for i in range(L)]
Sz = [model.lat.mps_sites()[i].Sz for i in range(L)]




# --- Translation-averaged spin-spin correlator ---
def avg_corr(psi, op_list, L, r):
    vals = []
    for R in range(L):
        i = R
        j = (R + r) % L  # periodic wrap-around
        # Get site index directly from the lattice
        val = psi.expectation_value_term([[i, op_list[i].site.index], [j, op_list[j].site.index]])  
        vals.append(val)
    return np.mean(vals)

def isotropic_corr(psi, Sx, Sy, Sz, L, lat):  # Added lat as an argument
    Cxx = [avg_corr(psi, Sx, L, r) for r in range(L)]
    Cyy = [avg_corr(psi, Sy, L, r) for r in range(L)]
    Czz = [avg_corr(psi, Sz, L, r) for r in range(L)]
    return (np.array(Cxx) + np.array(Cyy) + np.array(Czz)) / 3.0

# --- Compute and plot ---
C_iso = isotropic_corr(psi, Sx, Sy, Sz, L, lat)  # Pass lat to isotropic_corr
r = np.arange(len(C_iso))


plt.figure(figsize=(8, 5))
plt.plot(r, C_iso, 'o-', label='DMRG (PBC): Isotropic $C(r)$')
plt.xlabel('r')
plt.ylabel('C(r)')
plt.title(f'DMRG Isotropic Spin-Spin Correlation $C(r)$ (L = {L}, J2 = {J2})')
plt.grid(True)
plt.legend()
plt.tight_layout()
plt.show()

print("\nIsotropic spin-spin correlation C(r):")
for ri, ci in enumerate(C_iso):
    print(f"r = {ri:2d}, C(r) = {ci:.12f}")

It is giving the eoor

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'Array' object has no attribute 'site'

for the line

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val = psi.expectation_value_term([[i, op_list[i].site.index], [j, op_list[j].site.index]])

. I could not resolve the issue. Can someone please help me to solve this issue? Thank you very much!

[Jakob]

The code you pasted already fails before this line.

E.g.

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Sx = [model.lat.mps_sites().Sx for i in range(L)]

fails, as

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model.lat.mps_sites()

is a list.

The failure you report is expected behavior as well.
An operator, like the entries in your Sx list are Arrays and do not know what site they came from.
And even if the did, tenpy sites do not have an index attribute.

Try reading the docstring of the method you are using:
https://tenpy.readthedocs.io/en/latest/ ... value_term

and give it the parameters it actually requires.
You will find that you do not need to generate these lists of Sx, Sy, Sz and just give the expectation_value_term method the operator names.