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We present the TRIQS/Nevanlinna analytic continuation package, an efficient implementation of the methods proposed by J. Fei et al. (2021) [53] and (2021) [55]. TRIQS/Nevanlinna strives to provide a high quality open source (distributed under the GNU General Public License version 3) alternative to the more widely adopted Maximum Entropy based analytic continuation programs. With the additional Hardy functions optimization procedure, it allows for an accurate resolution of wide band and sharp features in the spectral function. Those problems can be formulated in terms of imaginary time or Matsubara frequency response functions. The application is based on the TRIQS C++/Python framework, which allows for easy interoperability with other TRIQS-based applications, electronic band structure codes and visualization tools. Similar to other TRIQS packages, it comes with a convenient Python interface.more » « less
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We introduce a Julia implementation of the recently proposed Nevanlinna analytic continuation method. The method is based on Nevanlinna interpolants and inherently preserves the causality of a response function due to its construction. For theoretical calculations without statistical noise, this continuation method is a powerful tool to extract real-frequency information from numerical input data on the Matsubara axis. This method has been applied to first-principles calculations of correlated materials. This paper presents its efficient and full-featured open-source implementation of the method including the Hamburger moment problem and smoothing.more » « less
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We present a temperature-extrapolation technique for self-consistent many-body methods, which provides a causal starting point for converging to a solution at a target temperature. The technique employs the Carathéodory formalism for interpolating causal matrix-valued functions and is applicable to various many-body methods, including dynamical mean-field theory, its cluster extensions, and self-consistent perturbative methods such as the self-consistent GW approximation. We show results that demonstrate that this technique can efficiently simulate heating and cooling hysteresis at a first-order phase transition, as well as accelerate convergence.more » « less
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We study the fluctuations responsible for pairing in the d -wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity solver. By analyzing how momentum- and frequency-dependent fluctuations generate the d -wave superconducting state in different representations, we identify antiferromagnetic fluctuations as the pairing glue of superconductivity in both the underdoped and the overdoped regime. Nevertheless, in the intermediate coupling regime, the predominant magnetic fluctuations may differ significantly from those described by conventional spin fluctuation theory.more » « less
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The Hubbard model is the simplest model of interacting fermions on a lattice and is of similar importance to correlated electron physics as the Ising model is to statistical mechanics or the fruit fly to biomedical science. Despite its simplicity, the model exhibits an incredible wealth of phases, phase transitions, and exotic correlation phenomena. Although analytical methods have provided a qualitative description of the model in certain limits, numerical tools have shown impressive progress in achieving quantitative accurate results over the past several years. This article gives an introduction to the model, motivates common questions, and illustrates the progress that has been achieved over recent years in revealing various aspects of the correlation physics of the model.more » « less
