New results in 1D repulsive Hubbard model: Quantum liquid, criticality and transport*

The Hubbard model, although extensively studied for a long time, has found renewed interest and become increasingly important in condensed matter physics, ultracold atoms and quantum metrology. In this talk, we will present new results of one-dimensional repulsive Hubbard model in the presence of a magnetic field. Using Bethe ansatz solution, we rigorously show that the fractional spin and holon excitations display different features of spin-charge separation in various phases regimes. We determine universal behavior of such spin-coherent and -incoherent liquids, Tan's contact and the interaction-driven criticality in and near different phases. In particular, analytical and general results on spin and charge Drude weights are obtained for the ground state, the Luttinger liquid and the quantum critical region at both zero and finite temperatures, showing deep insights into ballistic and diffusive quantum transports in strongly correlated systems in one dimension. References: Jia-Jia Luo, Han Pu and Xi-Wen Guan, Physical Review B 107, L201103 (2023); Jia-Jia Luo, Han Pu and Xi-Wen Guan, arXiv:2307.00890 Jia-Jia Luo, Han Pu, Xi-Wen Guan in preparation, 2023