Competing orders in the generalized Hund chain model at half filling

By using a combination of several nonperturbative techniques-a one-dimensional field theoretical approach together with numerical simulations using density-matrix renormalization group-we present an extensive study of the phase diagram of the generalized Hund model at half filling. This model encloses the physics of various strongly correlated one-dimensional systems, such as two-leg electronic ladders, ultracold degenerate fermionic gases carrying a large hyperfine spin 3/2, other cold gases such as ytterbium 171 or alkaline-earth condensates. A particular emphasis is laid on the possibility to enumerate and exhaust the eight possible Mott-insulating phases by means of a duality approach. We exhibit a one-to-one correspondence between these phases and those of the two-leg electronic ladders with interchain hopping. Our results obtained from a weak-coupling analysis are in remarkable quantitative agreement with our numerical results carried out at moderate coupling.