Exact results of one-dimensional repulsive Hubbard model

TL;DR

This paper provides exact analytical results for the one-dimensional repulsive Hubbard model, covering fractional excitations, thermodynamics, criticality, and quantum cooling, using Bethe Ansatz solutions.

Contribution

It offers the first rigorous analytical calculations of excitations, thermodynamics, and critical phenomena in the 1D Hubbard model with repulsive interactions.

Findings

Identification of fractionalized spinons and holons.

Explicit thermodynamic functions near quantum critical points.

Derivation of adiabatic cooling scheme based on Contact susceptibilities.

Abstract

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.