Gauge Symmetry

The gauge symmetry is defined by,

\(c_n \rightarrow e^{i\phi}c_n\) , \(c_n^\dagger \rightarrow e^{i\phi}c_n^\dagger\)

Terms in the Hamiltonian that do not change under this transformation 1. \(c_n^\dagger c_m\)(Hopping)

1. \(c_{n,\uparrow}^\dagger c_{n,\uparrow} - c_{n,\downarrow}^\dagger c_{n,\downarrow}\) (Magnetism)

2. \(c_{n,\uparrow}^\dagger c_{m,\downarrow}\) (Spin-Orbit Coupling)

3. \(c_{n,\uparrow}^\dagger c_{m,\uparrow} c_{n,\downarrow}^\dagger c_{m,\downarrow}\) (Interactions)