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.