XY Chain
Purpose and Hamiltonian
The anisotropic XY chain isolates $XX$ and $YY$ exchange:
$$ H=-J\sum_i\left[\frac{1+\gamma}{2}X_iX_{i+1} +\frac{1-\gamma}{2}Y_iY_{i+1}\right]-g\sum_iZ_i. $$
coupling is $J$, anisotropy is $\gamma$, and field is $g$.
$\gamma=0$ gives equal $XX$ and $YY$ couplings.
Basis and use
The dense computational-basis matrix has dimension $2^N$.
from quantum_lattice_models import xy_chain
H = xy_chain(n_sites=5, coupling=1.0, anisotropy=0.3, field=0.2)
Parameters
| Builder | Parameter | Type | Default | Constraint |
|---|---|---|---|---|
xy_chain |
n_sites |
int |
4 |
>= 1 |
xy_chain |
coupling |
float |
1.0 |
|
xy_chain |
anisotropy |
float |
0.3 |
|
xy_chain |
field |
float |
0.0 |
|
xy_chain |
periodic |
bool |
False |
User notes
The field sign differs from the general Heisenberg builder: this model uses $-g\sum Z_i$. Check conventions when comparing parameterizations.
Related: Ising chains, XXZ chain.