Exact SU(N) symmetry resolution of bosonic Hubbard models: general boson-fermion mappings and flat-band singlet-cluster states

We show how to perform exact diagonalization of SU(N)-symmetric Bose-Hubbard models separately in each irreducible representation of SU(N), by exploiting the Howe duality between U(L) and U(N). Three structural consequences follow for any lattice and any Hamiltonian built from the U(L) generators: (i) the spectrum in a given orbital sector is independent of N and of the particle statistics, (ii) the canonical partition functions for bosons and fermions obey the exact identity Z b(-N)=(-1) N bZ f(N), (iii) with unfrustrated hopping the groundstate is always a color ferromagnet, so that the color-resolved method we introduce is useful to study excited sectors, frustrated lattices and finite temperatures. As applications, we first derive the finite-temperature phase diagram of attractive SU(N) bosons on few-site rings at large N for arbitrary filling. We then show the emergence of singlet-cluster states from frustrated hopping, the counterpart of fermionic ferromagnetism, with the example of the sawtooth and kagome lattice.