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arXiv 0910.2805cond-mat.quant-gas
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周期性一维玻色气体中的亚稳量子相变:II。多体理论

Metastable quantum phase transitions in a periodic one-dimensional Bose gas: II. Many-body theory

R. Kanamoto, L. D. Carr, M. Ueda

摘要:

我们证明了Lieb-Liniger哈密顿量中的量子孤子正是yrast态。我们确定这样的解决方案清楚地与Lieb的II型激发从弱到强相互作用,澄清了一个长期存在的问题,这个激发分支的物理意义。我们证明了以前在弱相互作用的Lieb-Liniger哈密顿量的平均场分析中发现的亚稳量子相变[Phys. Rev. A { \bf 79},063616(2009)]扩展到周期性一维玻色气体的介质到强相互作用区域。我们的方法是精确对角化,有限大小的Bethe anomalies,和玻色子费米子映射的Tonks-Girardeau限制。

英文摘要:

We show that quantum solitons in the Lieb-Liniger Hamiltonian are precisely the yrast states. We identify such solutions clearly with Lieb's type II excitations from weak to strong interactions, clarifying a long-standing question of the physical meaning of this excitation branch. We demonstrate that the metastable quantum phase transition previously found in mean field analysis of the weakly-interacting Lieb-Liniger Hamiltonian [Phys. Rev. A {\bf 79}, 063616 (2009)] extends into the medium- to strongly-interacting regime of a periodic one-dimensional Bose gas. Our methods are exact diagonalization, finite-size Bethe ansatz, and the boson-fermion mapping in the Tonks-Girardeau limit.

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