Truncated configuration interaction expansions as solvers for correlated quantum impurity models and dynamical mean-field theory
Truncated configuration interaction expansions as solvers for correlated quantum impurity models and dynamical mean-field theory
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DOI：
10.1103/physrevb.86.165128
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发表时间：
2012-03
影响因子：
3.7
通讯作者：
D. Zgid;E. Gull;G. Chan
中科院分区：
文献类型：
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作者：
D. Zgid;E. Gull;G. Chan
相关量子杂质模型的多项式成本求解器的发展，具有可控的误差，是量子多体物理学的一个核心挑战，这些模型的应用范围从纳米科学到动态平均场理论（DMFT）。在这里，我们描述了如何配置相互作用（CI）近似精确对角化（艾德）可能被用作DMFT中的求解器。CI近似保留了艾德的主要优点，如处理一般相互作用和非对角杂交的能力，并获得真实的光谱信息，但多项式成本。此外，它们的误差可以通过监测作为CI层级的函数的物理量的收敛来控制。使用基准DMFT的应用程序，如单网站DMFT的一维Hubbard模型和2×2簇DMFT的二维Hubbard模型，我们表明，CI近似使我们能够获得接近精确的艾德的结果的一小部分的成本。这是真实的，在整个范围内的相互作用强度，包括“困难”的制度，如在pseudogap阶段的二维哈伯德模型。我们利用CI近似处理大量轨道的能力，证明了使用24-bath轨道表示的2×2簇DMFT中bath表示的收敛性。因此，CI近似形成了一个有前途的路线，以扩展艾德的问题，目前难以研究使用其他求解器，如连续时间量子蒙特卡罗，包括杂质模型与大量的轨道和一般的相互作用。
The development of polynomial cost solvers for correlated quantum impurity models, with controllable errors, is a central challenge in quantum many-body physics, where these models find applications ranging from nanoscience to the dynamical mean-field theory (DMFT). Here, we describe how configuration interaction (CI) approximations to exact diagonalization (ED) may be used as solvers in DMFT. CI approximations retain the main advantages of ED, such as the ability to treat general interactions and off-diagonal hybridizations and to obtain real spectral information, but are of polynomial cost. Furthermore, their errors can be controlled by monitoring the convergence of physical quantities as a function of the CI hierarchy. Using benchmark DMFT applications, such as single-site DMFT of the one-dimensional Hubbard model and 2×2 cluster DMFT of the two-dimensional Hubbard model, we show that CI approximations allow us to obtain near-exact ED results for a tiny fraction of the cost. This is true over the entire range of interaction strengths including “difficult” regimes, such as in the pseudogap phase of the two-dimensional Hubbard model. We use the ability of CI approximations to treat large numbers of orbitals to demonstrate convergence of the bath representation in the 2×2 cluster DMFT using a 24-bath orbital representation. CI approximations thus form a promising route to extend ED to problems that are currently difficult to study using other solvers such as continuous-time quantum Monte Carlo, including impurity models with large numbers of orbitals and general interactions.