Fractional excitations and spin-incoherent liquids in 1D Hubbard model*

The Hubbard model has become increasingly important in condensed matter physics, quantum metrology and quantum information. In this talk, we will discuss fractional excitations and spin-incoherent liquids in the 1D repulsive Fermi-Hubbard model with di erent magnetic elds and llings. Using Bethe ansatz solution, we rigorously show that the fractional spin and charge excitations display di erent features of spin-charge separation in various lling limits. For a dilute- lled lattice, the interplay between the charge and the spin degrees of freedom can disrupt the coherent Luttinger liquids of spin and charge, giving rise to the so-called spin-incoherent liquid. Whereas near the half-lling limit, the charge velocity is exponentially suppressed, which means that the system enters the quantum critical regime, thus there exists neither spin- nor charge-incoherent liquids. Furthermore, we determine universal behaviour of such spin-coherent and -incoherent liquids in the vicinities of different phase transitions.