Heisenberg Chain
Purpose and structure
The anisotropic nearest-neighbor Heisenberg chain supports independent $XX$, $YY$, and $ZZ$ couplings and a uniform longitudinal field. It is useful for spin correlations, symmetry studies, and exact-diagonalization benchmarks.
$$ H=\sum_i(J_xX_iX_{i+1}+J_yY_iY_{i+1}+J_zZ_iZ_{i+1}) +g\sum_iZ_i. $$
The package uses Pauli products directly and a positive sign for field.
Basis and scaling
The computational basis has dimension $2^N$. The builder returns a dense matrix with Pauli-term metadata.
Package use
from quantum_lattice_models import heisenberg_chain
H = heisenberg_chain(n_sites=5, jx=1.0, jy=0.8, jz=1.2, field=0.1)
Parameters
| Builder | Parameter | Type | Default | Constraint |
|---|---|---|---|---|
heisenberg_chain |
n_sites |
int |
4 |
>= 1 |
heisenberg_chain |
jx |
float |
1.0 |
|
heisenberg_chain |
jy |
float |
1.0 |
|
heisenberg_chain |
jz |
float |
1.0 |
|
heisenberg_chain |
field |
float |
0.0 |
|
heisenberg_chain |
periodic |
bool |
False |
Validation and cautions
Hermiticity and real spectra are tested. The isotropic limit is $J_x=J_y=J_z$. Sparse and fixed-magnetization construction remain roadmap work.
Related: XXZ chain, Heisenberg ladder.