量子团簇理论的求和规则和浴参数化
Sum-rules and bath-parametrization for quantum cluster theories
摘要：
我们分析了细胞动力学平均场论（CDMFT）和动力学团簇近似（DCA）.我们推导出精确的和规则的杂交功能，并给出例子DMFT，CDMFT和DCA。对于基于哈密顿量的杂质求解器，这些求和规则可以用于监控浴参数化的收敛性。我们进一步讨论了如何对称的集群自然导致分解成不可约的组件，它可以独立参数化的浴格林矩阵，并给出了一个明确的配方找到最佳浴参数化。作为基准，我们重新审视一维哈伯德模型。我们仔细分析的密度作为化学势的函数的演变，并发现，接近莫特过渡，集群大小的收敛是出乎意料的慢。在两个维度，我们发现，我们需要这么多的浴室网站，以获得一个可靠的参数化，Lanczos计算几乎是可行的，目前的计算机。对于这样的大型浴池，我们的适应性方法应该证明是至关重要的，找到一个可靠的浴缸参数化。
英文摘要：
We analyze cellular dynamical mean-field theory (CDMFT) and the dynamical cluster approximation (DCA). We derive exact sum-rules for the hybridization functions and give examples for DMFT, CDMFT, and DCA. For impurity solvers based on a Hamiltonian, these sum-rules can be used to monitor convergence of the bath-parametrization. We further discuss how the symmetry of the cluster naturally leads to a decomposition of the bath Green matrix into irreducible components, which can be parametrized independently, and give an explicit recipe for finding the optimal bath-parametrization. As a benchmark we revisit the one-dimensional Hubbard model. We carefully analyze the evolution of the density as a function of chemical potential and find that, close to the Mott transition, convergence with cluster size is unexpectedly slow. In two dimensions we find, that we need so many bath-sites to obtain a reliable parametrization that Lanczos calculations are hardly feasible with current computers. For such large baths our symmetry-adapted approach should prove crucial for finding a reliable bath-parametrization.
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