Particle number conservation and block structures in matrix product states

Abstract The eigenvectors of the particle number operator in second quantization are characterized by block sparsity their matrix product state representations. This is shown to generalize other classes operators. Imposing yields a scheme for conserving that commonly used applications physics. Operations on such structures, rank truncation, and implications numerical algorithms discussed. Explicit rank-reduced representations one- two-particle operators constructed operate only non-zero blocks states.