Physics – Condensed Matter – Quantum Gases
Scientific paper
2012-01-31
Phys. Rev. A 85, 043606 (2012)
Physics
Condensed Matter
Quantum Gases
12 pages, 11 figures
Scientific paper
10.1103/PhysRevA.85.043606
Using the thermodynamic Bethe ansatz equations we study the quantum phase diagram, thermodynamics and criticality of one-dimensional spin-1 bosons with strongly repulsive density-density and antiferromagnetic spin-exchange interactions. We analytically derive a high precision equation of state from which the Tomonaga-Luttinger liquid physics and quantum critical behavior of the system are computed. We obtain explicit forms for the scaling functions near the critical points yielding the dynamical exponent $z=2$ and correlation length exponent $\nu=1/2$ for the quantum phase transitions driven by either the chemical potential or the magnetic field. Consequently, we further demonstrate that quantum criticality of the system can be mapped out from the finite temperature density and magnetization profiles of the 1D trapped gas. Our results provide the physical origin of quantum criticality in a 1D many-body system beyond the Tomonaga-Luttinger liquid description.
Batchelor Murray T.
Foerster Angela
Guan X.-W.
Kuhn Carlos C. N.
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