The concept of phase space crystal can be extended to systems of interacting particles where it refers to the many-body state having a solid-like crystalline structure in phase space. In this case, the interaction of particles plays an important role. In real space, the many-body Hamiltonian subjected to a perturbative periodic drive (with period T ) is given by H = ∑ ∑ i H ( x i , p i , t ) + ∑ ∑ i < j V ( x i − − x j ) . Usually, the interaction potential V ( x i − − x j ) is a function of two particles' distance in real space. By transforming to the rotating frame with the driving frequency and adapting rotating wave approximation (RWA), one can get the effective Hamiltonian. H R W A = ∑ ∑ i H R W A ( X i , P i , t ) + ∑ ∑ i < j U ( X i , P i ; X j , P j ) . Here, X i , P i are the stroboscopic position and momentum of i -th particle, namely, they take the values of x i ( t ) , p i ( t ) at the integer multiple of driving period t = n T . To have the crystal structure in phase space, the effective interaction in phase space needs to be invariant under the discrete rotational or translational operations in phase space.