Spin incoherent liquid and interaction-driven criticality in 1D Hubbard model

A rigorous understanding of the spin incoherent Tomonaga-Luttinger liquid (TLL), which displays solely a propagating charge mode but not a spin mode, and the interaction-driven quantum phase transitions in one-dimensional (1D) systems still remain elusive. In this Letter, we report the universal properties of spin incoherent TLL and interaction-driven criticality of the 1D repulsive Hubbard model by means of fractional charge and spin excitations, asymptotic of correlation functions as well as the lattice Contact. We build up an essential connection of Contact susceptibilities to the variations of density, magnetization and entropy with respect to the interaction strength, providing a rigorous understanding of interaction-driven phase transitions, Mott insulator and quantum cooling in the model. These relations hold true for higher dimensional systems.Comment: 4 figures 6 page

Exact results of one-dimensional repulsive Hubbard model

We present analytical results of fundamental properties of one-dimensional (1D) Hubbard model with a repulsive interaction, ranging from fractional excitations to universal thermodynamics, interaction-driven criticality, correlation functions, Contact susceptibilities and quantum cooling. 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. Based on the analysis on the fractional charge and spin excitations, the spin-incoherent Luttinger liquid 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. Near quadruple critical point, we then further analytically obtain the thermodynamical properties, dimensionless ratios and scaling functions near quantum phase transitions in terms of chemical potential, magnetic field and interaction. In particular, we determine additivity rules of spin and charge susceptibilities, and derive explicit forms of thermodynamics of spin-incoherent Luttinger liquid. Finally, in order to capture deeper insight into the Mott insulator and interaction driven criticality, we further study the double occupancy and its associated Contact and Contact susceptibilities through which an adiabatic cooling scheme upon the quantum criticality is introduced.Comment: slight changes, 50 pages +18 figures, new analytical result

A Model of Two-Way Selection System for Human Behavior

We propose a model of two-way selection system. It appears in the processes like choosing a mate between men and women, making contracts between job hunters and recruiters, and trading between buyers and sellers. In this paper, we propose a model of two-way selection system, and present its analytic solution for the expectation of successful matching total and the regular pattern that the matching rate trends toward an inverse proportion to either the ratio between the two sides or the ratio of the state total to the smaller people number. The proposed model is verified by empirical data of the matchmaking fairs. Results indicate that the model well predicts this typical real-world two- way selection behavior to the bounded error extent, thus it is helpful for understanding the dynamics mechanism of the real-world two-way selection system.Comment: 8 pages, 4 figure