Exact results of one-dimensional repulsive Hubbard model.

Abstract

We present analytical results of fundamental properties of one-dimensional (1D) Hubbard model with a repulsive interaction.
New results of the model with arbitrary external fields include:
 I) Using the exact solutions of the Bethe Ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. We then investigate the gapped excitations in terms of the spin string and the $k-\Lambda$ string bound states at arbitrary driving fields, showing subtle differences of spin magnons and charge $\eta$-pair excitations. 
II) For a high density and high spin magnetization region, i.e. near the quadruple critical point, we further analytically obtain the thermodynamical properties, dimensionless ratios and scaling functions near quantum phase transitions.
 III) Importantly, we give the general scaling functions at quantum criticality for arbitrary filling
and interaction strength. These can directly apply to other integrable models. 
IV) Based on the fractional excitations and the scaling laws, the spin-incoherent Luttinger liquid (SILL) with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of the conformal field theory. We also for the first time obtain the analytical result of the thermodynamics for the SILL.
V) Finally, in order to capture deeper insight into the Mott insulator and interaction-driven criticality, we further study the double occupancy and propose its associated Contact and Contact susceptibilities through which an adiabatic cooling scheme based upon quantum criticality is proposed. In this scenario, we build up general relations among arbitrary external and internal potential driven quantum phase transitions, providing a comprehensive understanding of quantum criticality. Our methods offer rich perspectives of quantum integrability and offer promising guidance to future experiments with interacting electrons and ultracold atoms both with and without a lattice.