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摘要翻译：
一维相互作用玻色子的精确可解的Lieb-Liniger模型引起了新的兴趣，因为目前的超冷原子实验开始探索这个区域。在这里，我们数值求解了由多达20个粒子的有限尺寸系统中的精确多体波函数的Bethe ansatz解引起的方程。我们讨论了这些解的新特征，以及它们在有限密度下如何偏离著名的弦解[H.B.Thacker,Rev.Mod.Phys.\\TextBF{53},253(1981)]。我们给出了强相互作用极限下的激发态弦解，讨论了它们的物理解释，以及在平均场极限下发生的随相互作用强度变化的量子相变的特征。最后，我们将我们的结果与截断基下多体哈密顿量精确对角化的结果进行了比较。我们还给出了一维排斥玻色气体在环上的激发态解和激发谱。
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英文标题：
《Excitation spectrum of bosons in a finite one-dimensional circular
waveguide via the Bethe ansatz》
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作者：
Andrew G. Sykes, Peter D. Drummond and Matthew J. Davis
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Other Condensed Matter 其他凝聚态物质
分类描述：Work in condensed matter that does not fit into the other cond-mat classifications
在不适合其他cond-mat分类的凝聚态物质中工作
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
The exactly solvable Lieb-Liniger model of interacting bosons in one-dimension has attracted renewed interest as current experiments with ultra-cold atoms begin to probe this regime. Here we numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss the novel features of the solutions, and how they deviate from the well-known string solutions [H. B. Thacker, Rev. Mod. Phys.\ \textbf{53}, 253 (1981)] at finite densities. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Finally we compare our results to those of exact diagonalization of the many-body Hamiltonian in a truncated basis. We also present excited state solutions and the excitation spectrum for the repulsive 1D Bose gas on a ring.
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PDF链接：
https://arxiv.org/pdf/707.2422
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