1,662
edits
(Added free to read link in citations with OAbot #oabot) 
m (→The Hamiltonian: deleted word "regular" which doesn't mean anything specific here and may fool readers into thinking it's a technical term) 

<math> H = t \sum_{ \left\langle i, j \right\rangle } \hat{b}^{\dagger}_i \hat{b}_j + \frac{U}{2} \sum_{i} \hat{n}_i \left( \hat{n}_i  1 \right)  \mu \sum_i \hat{n}_i </math>.
Here, <math>\left\langle i, j \right\rangle</math> denotes summation over all neighboring lattice sites <math>i</math> and <math>j</math>, while <math>\hat{b}^{\dagger}_i</math> and <math>\hat{b}^{}_i</math> are
This Hamiltonian has a global <math>U(1)</math> symmetry, which means that it is invariant (i.e. its physical properties are unchanged) by the transformation <math>\hat{b}_i \rightarrow e^{i \theta} \hat{b}_i</math>. In a [[Superfluiditysuperfluid]] phase, this symmetry is [[Spontaneous symmetry breakingspontaneously broken]].
