二次能量Luttinger液体的动态结构因子 色散与长程相互作用

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摘要翻译：
我们计算了二次能量色散K^2/2m和长程密度-密度相互作用的一维无自旋费米子的动力学结构因子S(omega，q)，其f_q由小动量转移q<<q_0<<K_f控制。这里q0是动量转移截止，而kf是费米动量。利用泛函玻色化和已知的对称闭费米子环的性质，我们得到了在小参数q0/kf中逆不可约极化向二阶的扩展。与基于常规玻色子化的微扰理论相比，我们的泛函玻色子化方法不受质量壳奇异性的困扰。对于f_q=f_0+f_0^{2}Q_2/2+O(q^4)与有限f_0^{2}的相互作用，我们证明了动量标度q_c=1/mF_0^{2}将两个系统分开，这两个系统的特征与集合零声模的宽度gamma_q和S(omega，q)的其他特征具有不同的q依赖性。对于q_c<<q<<k_F，我们发现该区域中的线形是非洛伦兹线形，其总宽度为q^3/(m，q_c)阶，且在下边有一个阈值奇点。
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英文标题：
《Dynamic structure factor of Luttinger liquids with quadratic energy
  dispersion and long-range interactions》
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作者：
Peyman Pirooznia, Florian Schuetz, and Peter Kopietz
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Strongly Correlated Electrons        强关联电子
分类描述：Quantum magnetism, non-Fermi liquids, spin liquids, quantum criticality, charge density waves, metal-insulator transitions
量子磁学，非费米液体，自旋液体，量子临界性，电荷密度波，金属-绝缘体跃迁
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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：
  We calculate the dynamic structure factor S (omega, q) of spinless fermions in one dimension with quadratic energy dispersion k^2/2m and long range density-density interaction whose Fourier transform f_q is dominated by small momentum-transfers q << q_0 << k_F. Here q_0 is a momentum-transfer cutoff and k_F is the Fermi momentum. Using functional bosonization and the known properties of symmetrized closed fermion loops, we obtain an expansion of the inverse irreducible polarization to second order in the small parameter q_0 / k_F. In contrast to perturbation theory based on conventional bosonization, our functional bosonization approach is not plagued by mass-shell singularities. For interactions which can be expanded as f_q = f_0 + f_0^{2} q^2/2 + O (q^4) with finite f_0^{2} we show that the momentum scale q_c = 1/ | m f_0^{2} | separates two regimes characterized by a different q-dependence of the width gamma_q of the collective zero sound mode and other features of S (omega, q). For q_c << q << k_F we find that the line-shape in this regime is non-Lorentzian with an overall width gamma_q of order q^3/(m q_c) and a threshold singularity at the lower edge.
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PDF链接：
https://arxiv.org/pdf/802.097

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