SSH Model
Purpose and structure
The Su-Schrieffer-Heeger chain has $A$ and $B$ sites in each unit cell, with intracell hopping $t_1$ and intercell hopping $t_2$:
$$ H=-\sum_m(t_1|m,A\rangle\langle m,B| +t_2|m+1,A\rangle\langle m,B|+\mathrm{h.c.}). $$
For open boundaries and $|t_1|<|t_2|$, finite chains support near-zero edge-localized states.
Basis and use
The single-particle dimension is $2N_c$.
from quantum_lattice_models import ssh_model
H = ssh_model(n_cells=12, t1=0.4, t2=1.0)
Parameters
| Builder | Parameter | Type | Default | Constraint |
|---|---|---|---|---|
ssh_model |
n_cells |
int |
8 |
>= 1 |
ssh_model |
t1 |
float |
0.5 |
|
ssh_model |
t2 |
float |
1.0 |
|
ssh_model |
periodic |
bool |
False |
Validation and cautions
The decoupled-dimer spectrum and topological edge localization are tested. This is a finite real-space model; winding numbers require future Bloch support.
Related: Rice-Mele model, Kitaev BdG chain.