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We study by the strong disorder renormalization group (RG) method thelow-energy properties of the one-dimensional Hubbard model with random-hoppingmatrix-elements $t_{min}<t<t_{max}$, and with random on-site Coulomb repulsionterms $0 \le U_{min}<U<U_{max}$. There are two critical phases, correspondingto an infinite randomness spin random singlet for strong interactions ($U_{min}> t_{max}$) and to an orbital infinite randomness fixed point for vanishinginteractions ($U_{max}/t_{max} \to 0$). To each critical infinite randomnessfixed point is connected a Griffiths phase, the correlation length anddynamical exponent of which have well defined asymptotic dependences on thecorresponding quantum control parameter. The theoretical predictions for thescaling in the vicinity of the critical points compare well to numerical RGsimulations.Comment: 9 pages, 7 figure

Strongly disordered Hubbard model in one dimension: Spin and orbital infinite randomness and Griffiths phases