Continuous-time auxiliary-field Monte Carlo for quantum impurity models

formula omitted]QIST v0.7: An open source continuous-time quantum Monte Carlo impurity solver toolkit

We describe the use of coupled-cluster theory as an impurity solver in dynamical mean-field theory (DMFT) and its cluster extensions. We present numerical results at the level of coupled-cluster theory with single and double excitations (CCSD) for the density of states and self-energies of cluster impurity problems in the one- and two-dimensional Hubbard models. Comparison to exact diagonalization shows that CCSD produces accurate density of states and self-energies at a variety of values of $U/t$ and filling fractions. However, the low cost allows for the use of many bath sites, which we define by a discretization of the hybridization directly on the real frequency axis. We observe convergence of dynamical quantities using approximately 30 bath sites per impurity site, with our largest 4-site cluster DMFT calculation using 120 bath sites. We suggest coupled cluster impurity solvers will be attractive in ab initio formulations of dynamical mean-field theory.

Dynamical mean-field theory (DMFT) studies frequently observe a fine structure in the local spectral function of the SU(2) Fermi-Hubbard model at half filling: In the metallic phase close to the Mott transition, subpeaks emerge at the inner edges of the Hubbard bands. Here we demonstrate that these subpeaks originate from the low-energy effective interaction of doublon-holon pairs, by investigating how the correlation functions of doublon and holon operators contribute to the subpeaks. A mean-field analysis of the low-energy effective Hamiltonian provides results consistent with our DMFT calculation using the numerical renormalization group as an impurity solver. In the SU(3) and SU(4) Hubbard models, the subpeaks become more pronounced due to the increased degeneracy of doublon-holon pair excitations.

Several recent works have introduced highly compact representations of single-particle Green's functions in the imaginary time and Matsubara frequency domains, as well as efficient interpolation grids used to recover the representations. In particular, the intermediate representation with sparse sampling and the discrete Lehmann representation (DLR) make use of low rank compression techniques to obtain optimal approximations with controllable accuracy. We consider the use of the DLR in dynamical mean-field theory (DMFT) calculations, and in particular show that the standard full Matsubara frequency grid can be replaced by the compact grid of DLR Matsubara frequency nodes. We test the performance of the method for a DMFT calculation of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ at temperature $50\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ using a continuous-time quantum Monte Carlo impurity solver, and demonstrate that Matsubara frequency quantities can be represented on a grid of only 36 nodes with no reduction in accuracy, or increase in the number of self-consistent iterations, despite the presence of significant Monte Carlo noise.

Dynamical mean-field theory calculation with the dynamical density-matrix renormalization group

Ab-initio density functional theory (DFT)＋U has been used to study the spin-resolved electronic band structure and the partial density of states of the multiferroic XY-antiferromagnetic Ba2CoGe2O7. Using the constrained random-phase approximation (cRPA) method, the value of Hubbard U and Hund’s coupling JH has been determined and plugged into the further dynamical mean field theory (DMFT) calculations. The strong metal-ligand hybridization between Co-3d and O-2p orbitals in the CoO4 tetrahedron has been demonstrated via DFT and DFT＋DMFT calculations. The calculated indirect band gap in the antiferromagnetic state without and with U (=5 eV) correction is found to be 0.67 and 2.71 eV, respectively. The highest calculated ordered magnetic moment of 2.7 μB/Co2+ is close to the reported experimental value. The presented DFT calculations based on the different orbital models brings the underlying strong electronic correlation in the Ba2CoGe2O7.

In condensed matter physics, the idea of localized magnetic moments and the scattering of conduction electrons by those local moments are of central importance not only for explaining the transport of electrons at low temperature region but also for developing the related models and theories to extend our understanding of novel physics like non-conventional superconductor, quantum phase transition and non-Fermi liquid behavior. In the first chapter of this work, I will look back at the discovery of Kondo scattering, the introduction of Anderson impurity scenario, the extension to lattice version of the Anderson impurities, the periodic Anderson model, and how these ideas are used to the heavy fermion materials. In order to attack those problems and models numerically, in the second chapter, I will discuss the algorithm of dynamical mean-field theory, where interaction expansion continuous time quantum Monte Carlo is used as impurity solver. The introduction of dynamical mean-field theory and its related methods are one of the largest victory of computational condensed matter physics in the past three decades. By mapping the lattice problem to an impurity problem and solving it self-consistently, we can get the static and dynamic outputs in the thermal dynamical limit from dynamical mean-field theory simulation by solving a single site problem. In the infinite coordinate number limit, the dynamical mean-field theory results converge to the exact results. Quantum Monte Carlo is widely used in computational physics. Compared with the conventional quantum Monte Carlo, the recently introduced interaction expansion continuous time quantum Monte Carlo is free of decomposition error in imaginary time. In the third chapter, the effect of phonon coupling to the conduction band of the periodic Anderson model is discussed. In the periodic Anderson model at low temperature region, the local moments on f -band are screened by the conduction electrons and form the coherent Kondo singlet states. When the lattice oscillation degree of freedom is introduced to the conduction band, the conduction electrons bond with each other because of the retarded attractive interaction incurred by the phonons. As the electron-phonon interaction is large, the competition of electronic bonding on the c -band will compete with the Kondo singlet bonding between the conduction electrons and the local moments and finally lead to a Kondo collapse. In the fourth chapter, the pressure induced volume collapse problem of Cerium is explored. It has been discovered that Cerium will experience a 15% volume collapse from a

Pyqcm is a Python/C++ library that implements a few quantum cluster methods with an exact diagonalization impurity solver. Quantum cluster methods are used in the study of strongly correlated electrons to provide an approximate solution to Hubbard-like models. The methods covered by this library are Cluster Perturbation Theory (CPT), the Variational Cluster Approach (VCA) and Cellular (or Cluster) Dynamical Mean Field Theory (CDMFT). The impurity solver (the technique used to compute the cluster’s interacting Green function) is exact diagonalization from sparse matrices, using the Lanczos algorithm and variants thereof. The core library is written in C++ for performance, but the interface is in Python, for ease of use and inter-operability with the numerical Python ecosystem. The library is distributed under the GPL license.

Pyqcm is a Python/C++ library that implements a few quantum cluster methods with an exact diagonalization impurity solver. Quantum cluster methods are used in the study of strongly correlated electrons to provide an approximate solution to Hubbard-like models. The methods covered by this library are Cluster Perturbation Theory (CPT), the Variational Cluster Approach (VCA) and Cellular (or Cluster) Dynamical Mean Field Theory (CDMFT). The impurity solver (the technique used to compute the cluster’s interacting Green function) is exact diagonalization from sparse matrices, using the Lanczos algorithm and variants thereof. The core library is written in C++ for performance, but the interface is in Python, for ease of use and inter-operability with the numerical Python ecosystem. The library is distributed under the GPL license.

The dynamical mean field theory (DMFT), which is successful in the study of strongly correlated fermions, was recently extended to boson systems [Phys. Rev. B {\textbf 77}, 235106 (2008)]. In this paper, we employ the bosonic DMFT to study the Bose-Hubbard model which describes on-site interacting bosons in a lattice. Using exact diagonalization as the impurity solver, we get the DMFT solutions for the Green's function, the occupation density, as well as the condensate fraction on a Bethe lattice. Various phases are identified: the Mott insulator, the Bose-Einstein condensed (BEC) phase, and the normal phase. At finite temperatures, we obtain the crossover between the Mott-like regime and the normal phase, as well as the BEC-to-normal phase transition. Phase diagrams on the $\mu/U-\tilde{t}/U$ plane and on the $T/U-\tilde{t}/U$ plane are produced ($\tilde{t}$ is the scaled hopping amplitude). We compare our results with the previous ones, and discuss the implication of these results to experiments.

We investigate the nature of the 5⁢𝑓 electrons in the unconventional odd-parity superconductor UTe$_2$, focusing on the degree of covalency, localization versus itinerancy, and dominant electronic configuration. This is achieved using density functional theory (DFT) in combination with dynamical mean-field theory (DMFT) calculations. A key aspect of our approach is the material-specific tuning of the double-counting correction parameter, $𝜇_{dc}$, within the DFT+DMFT part. This tuning is guided by the energy dependence of photoionization cross sections in valence band photoelectron spectroscopy. The reliability of the parameters is confirmed by the accurate reproduction of the angle-resolved valence-band photoemission spectra and the U4⁢𝑓core-level data. The DFT+DMFT model reveals that in UTe$_2$ U5⁢𝑓$^𝑛$ configurations with 𝑛=1–4 contribute to the ground state, with the 5⁢𝑓$^2$configuration being most prevalent and an average 5⁢𝑓 shell filling close to 2.5. The model further suggests that the 5⁢𝑓 electrons form narrow bands and that charge fluctuations due to degeneracy play a role in addition to coherent valence dynamics arising from hybridization with the conduction bath. Additionally, the significance of the U6⁢𝑑 states in UTe$_2$ is discussed.

We investigate the effect of charge self-consistency (CSC) in density\nfunctional theory plus dynamical mean-field theory (DFT+DMFT) calculations\ncompared to simpler "one-shot" calculations for materials where interaction\neffects lead to a strong redistribution of electronic charges between different\norbitals or between different sites. We focus on two systems close to a\nmetal-insulator transition, for which the importance of CSC is currently not\nwell understood. Specifically, we analyze the strain-related orbital\npolarization in the correlated metal CaVO$_3$ and the spontaneous electronic\ncharge disproportionation in the rare-earth nickelate LuNiO$_3$. In both cases,\nwe find that the CSC treatment reduces the charge redistribution compared to\ncheaper one-shot calculations. However, while the MIT in CaVO$_3$ is only\nslightly shifted due to the reduced orbital polarization, the effect of the\nsite polarization on the MIT in LuNiO$_3$ is more subtle. Furthermore, we\nhighlight the role of the double-counting correction in CSC calculations\ncontaining different inequivalent sites.\n

Recent discoveries of various novel iron oxides and hydrides, which become stable at very high pressure and temperature, are extremely important for geoscience. In this paper, we report the results of an investigation on the electronic structure and magnetic properties of the hydride FeOH, using density functional theory plus dynamical mean-field theory (DFT+DMFT) calculations. An increase in the hydrogen concentration resulted in the destruction of dimeric oxygen pairs and, hence, a specific band structure of FeO with strongly hybridized Fe--O- anti-bonding molecular orbitals, which led to a metallic state with the Fe ions at nearly 3+. Increasing the H concentration resulted in effective mass enhancement growth which indicated an increase in the magnetic moment localization. The calculated static momentum-resolved spin susceptibility demonstrated that an incommensurate antiferromagnetic (AFM) order was expected for FeO, whereas strong ferromagnetic (FM) fluctuations were observed for FeOH.

By means of density functional theory plus dynamical mean-field theory (DFT+DMFT) calculations and resonant inelastic x-ray scattering (RIXS) experiments, we investigate the high-pressure phases of the spin-orbit-coupled $J_{\rm{eff}}=3/2$ insulator GaTa$_4$Se$_8$. Its metallic phase, derived from the Mott state by applying pressure, is found to carry $J_{\rm{eff}}=3/2$ moments. The characteristic excitation peak in the RIXS spectrum maintains its destructive quantum interference of $J_{\rm{eff}}$ at the Ta $L_2$-edge up to 10.4 GPa. Our exact diagonalization based DFT+DMFT calculations including spin-orbit coupling also reveal that the $J_{\rm{eff}}=3/2$ character can be clearly identified under high pressure. These results establish the intriguing nature of the correlated metallic magnetic phase, which represents the first confirmed example of $J_{\rm{eff}}$=3/2 moments residing in a metal. They also indicate that the pressure-induced superconductivity is likely unconventional and influenced by these $J_{\rm{eff}}=3/2$ moments. Based on a self-energy analysis, we furthermore propose the possibility of doping-induced superconductivity related to a spin-freezing crossover.

We apply a recently introduced hybridization-flow functional renormalization group scheme for Anderson-like impurity models as an impurity solver in a dynamical mean-field theory (DMFT) approach to lattice Hubbard models. We present how this scheme is capable of reproducing metallic and insulating solutions of the lattice model. Our setup also offers a numerically rather inexpensive method to calculate two-particle correlation functions. For the paramagnetic Hubbard-model on the Bethe lattice in infinite dimensions we calculate the local two-particle-vertex for the metallic and the insulating phase. Then we go to a two-site cluster-DMFT-scheme for the two-dimensional Hubbard-model that includes short-range antiferromagnetic fluctuations and obtain the local and non-local two-particle-vertex-functions. We discuss the rich frequency structures of these vertices and compare with the vertex in the single-site solution.