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Practical consequences of the Luttinger-Ward functional multivaluedness for cluster DMFT methods

机译：Luttinger-Ward函数多值对集群DMFT方法的实际影响

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摘要

The Luttinger-Ward functional (LWF) has been a starting point for conserving approximations in many-body physics for 50 years. The recent discoveries of its multivaluedness and the associated divergence of the two-particle irreducible vertex function Γ have revealed an inherent limitation of this approach. Here we demonstrate how these undesirable properties of the LWF can lead to a failure of computational methods based on an approximation of the LWF. We apply the nested cluster scheme (NCS) to the Hubbard model and observe the existence of an additional stationary point of the self-consistent equations, associated with an unphysical branch of the LWF. In the strongly correlated regime, starting with the first divergence of Γ, this unphysical stationary point becomes attractive in the standard iterative technique used to solve DMFT. This leads to an incorrect solution, even in the large cluster size limit, for which we discuss diagnostics.
机译：Luttinger-Ward函数（LWF）成为保存多体物理学近似值的起点已有50年了。最近对其多值性和两粒子不可约顶点函数Γ的相关发散的发现揭示了这种方法的固有局限性。在这里，我们演示了LWF的这些不良特性如何导致基于LWF近似的计算方法的失败。我们将嵌套聚类方案（NCS）应用于Hubbard模型，并观察到与LWF的非物理分支相关的自洽方程组的其他固定点的存在。在高度相关的方案中，从Γ的第一个发散开始，这种非物理的固定点在用于解决DMFT的标准迭代技术中变得有吸引力。即使在较大的群集大小限制下，这也会导致错误的解决方案，我们将讨论诊断问题。

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  • 来源
    《Physical review》 |2018年第12期|125141.1-125141.24|共24页
  • 作者

    J. Vucicevic; N. Wentzell; M. Ferrero; O. Parcollet;

  • 作者单位

    Institut de Physique Theorique (IPhT), CEA, CNRS, UMR 3681, 91191 Gif-sur-Yvette, France,Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118,11080 Belgrade, Serbia;

    Institut de Physique Theorique (IPhT), CEA, CNRS, UMR 3681, 91191 Gif-sur-Yvette, France;

    Centre de Physique Theorique, Ecole Polytechnique,CNRS, Universite Paris-Saclay, 91128 Palaiseau, France,College de France, 11 place Marcelin Berthelot, 75005 Paris, France;

    Institut de Physique Theorique (IPhT), CEA, CNRS, UMR 3681, 91191 Gif-sur-Yvette, France;

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