Noschang Kuhn, CarlosGuan, Xi-WenFoerster, AngelaBatchelor, Murray2015-12-081050-2947http://hdl.handle.net/1885/31599We investigate universal thermodynamics and quantum criticality of spin-1 bosons with strongly repulsive density-density and antiferromagnetic spin-exchange interactions in a one-dimensional harmonic trap. From the equation of state, we find that a partially polarized core is surrounded by two wings composed of either spin-singlet pairs or a fully spin-aligned Tonks-Girardeau gas depending on the polarization. We describe how the scaling behavior of density profiles can reveal the universal nature of quantum criticality and map out the quantum phase diagram. We further show that at quantum criticality the dynamical critical exponent z=2 and correlation length exponent ν=1/2. This reveals a subtle resemblance to the physics of the spin-1/2 attractive Fermi gas.Author/s retain copyrightKeywords: Antiferromagnetics; Correlation lengths; Density profile; Dynamical critical exponent; Equation of state; Fermi gas; One-dimensional harmonic trap; Quantum criticality; Quantum phase diagrams; Scaling behavior; Spin-exchange interaction; Tonks-Girardeau g201210.1103/PhysRevA.86.0116052016-02-24