Quantum criticality of spin-1 bosons in a 1D harmonic trap

Details Quantum criticality of spin-1 bosons in a 1D harmonic trap Quantum criticality of spin-1 bosons in a 1D harmonic trap

2011-11-10

arxiv.org/abs/1111.2375v1

Physics

Condensed Matter

Quantum Gases

4 pages, 6 figures

Scientific paper

Using the thermodynamic Bethe ansatz equations, we derive the equation of state of spin-1 bosons with strongly repulsive density-density and antiferromagnetic spin-exchange interactions. In an harmonic trap we find that a partially-polarized core is surrounded by two wings composed of either spin-singlet bosonic pairs or a fully spin-aligned Tonks-Girardeau gas. The universal scaling functions yield the same dynamical exponent $z=2$ and correlation length exponent $\nu=1/2$ for the thermodynamic properties of these different spin states. This reveals a subtle resemblance to the physics of the spin-1/2 attractive Fermi gas. We demonstrate that the phase diagram, the Tomonaga-Luttinger liquids and critical properties of the bulk system can be mapped out from the density profiles of the trapped spinor gas at finite temperatures.

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