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Bosonic self-energy functional theory

机译：玻色子自能泛函理论

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We derive the self-energy functional theory for bosonic lattice systems with broken U(l) symmetry by parametrizing the bosonic Baym-Kadanoff effective action in terms of one- and two-point self-energies. The formalism goes beyond other approximate methods such as the pseudoparticle variational cluster approximation, the cluster composite boson mapping, and the Bogoliubov+U theory. It simplifies to bosonic dynamical-mean-field theory when constraining to local fields, whereas when neglecting kinetic contributions of noncondensed bosons, it reduces to the static mean-field approximation. To benchmark the theory, we study the Bose-Hubbard model on the two- and three-dimensional cubic lattice, comparing with exact results from path integral quantum Monte Carlo. We also study the frustrated square lattice with next-nearest-neighbor hopping, which is beyond the reach of Monte Carlo simulations. A reference system comprising a single bosonic state, corresponding to three variational parameters, is sufficient to quantitatively describe phase boundaries and thermodynamical observables, while qualitatively capturing the spectral functions, as well as the enhancement of kinetic fluctuations in the frustrated case. On the basis of these findings, we propose self-energy functional theory as the omnibus framework for treating bosonic lattice models, in particular, in cases where path integral quantum Monte Carlo methods suffer from severe sign problems (e.g., in the presence of nontrivial gauge fields or frustration). Self-energy functional theory enables the construction of diagrammatically sound approximations that are quantitatively precise and controlled in the number of optimization parameters but nevertheless remain computable by modest means.
机译：我们通过参数化一点和两点自能量的Bosonic Baym-Kadanoff有效作用来推导具有破碎的U（l）对称性的Bosonic晶格系统的自能量泛函理论。形式主义超越了其他近似方法，例如伪粒子变分簇近似，簇复合玻色子映射和Bogoliubov + U理论。当约束于局部场时，它简化为玻色动力学平均场理论，而当忽略非凝聚玻色子的动力学贡献时，则简化为静态平均场近似。为了验证该理论，我们对二维和三维立方晶格上的Bose-Hubbard模型进行了研究，并与路径积分量子蒙特卡洛的精确结果进行了比较。我们还研究了最近邻跳频导致的受挫方格，这是蒙特卡洛模拟无法实现的。包含与三个变化参数相对应的单个玻色状态的参考系统足以定量描述相界和热力学观测值，同时定性地捕获频谱函数，并在受挫情况下增强动态波动。基于这些发现，我们提出将自能量泛函理论作为用于处理玻色子晶格模型的综合框架，特别是在路径积分量子蒙特卡洛方法遭受严重符号问题（例如，存在非平凡标尺）的情况下字段或无奈）。自能量泛函理论可以构建合理的图示近似值，该近似值在定量上是精确的，并且可以通过优化参数的数量进行控制，但是仍然可以通过适度的方式进行计算。

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  • 来源
    《Physical review》 |2016年第19期|195119.1-195119.21|共21页
  • 作者

    Dario Huegel; Philipp Werner; Lode Pollet; Hugo U. R. Strand;

  • 作者单位

    Department of Physics, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universitaet Muenchen, Theresienstrasse 37, 80333 Munich, Germany;

    Department of Physics, University of Fribourg,1700 Fribourg, Switzerland;

    Department of Physics, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universitaet Muenchen, Theresienstrasse 37, 80333 Munich, Germany;

    Department of Physics, University of Fribourg,1700 Fribourg, Switzerland;

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