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Physical review. B./Physical review. B

Correlation matrix renormalization theory for correlated-electron materials with application to the crystalline phases of atomic hydrogen

Xin Zhao, Jun Liu, Yongxin Yao, Cai‐Zhuang Wang, Kai‐Ming Ho

Published Feb 23, 2018• 8 citations
Publisher

Abstract

Developing accurate and computationally efficient methods to calculate the electronic structure and total energy of correlated-electron materials has been a very challenging task in condensed matter physics and materials science. Recently, we have developed a correlation matrix renormalization (CMR) method which does not assume any empirical Coulomb interaction $U$ parameters and does not have double counting problems in the ground-state total energy calculation. The CMR method has been demonstrated to be accurate in describing both the bonding and bond breaking behaviors of molecules. In this study, we extend the CMR method to the treatment of electron correlations in periodic solid systems. Using a linear hydrogen chain as a benchmark system, we show that the results from the CMR method compare very well with those obtained recently by accurate quantum Monte Carlo (QMC) calculations. We also study the equation of states of three-dimensional crystalline phases of atomic hydrogen. We show that the results from the CMR method agree much better with the available QMC data in comparison with those from density functional theory and Hartree-Fock calculations.

DOI
10.1103/physrevb.97.075142

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Developing accurate and computationally efficient methods to calculate the electronic structure and total energy of correlated-electron materials has been a very challenging task in condensed matter physics and materials science. Recently, we have developed a correlation matrix renormalization (CMR) method which does not assume any empirical Coulomb interaction UUU parameters and does not have double counting problems in the ground-state total energy calculation. The CMR method has been demonstrated to be accurate in describing both the bonding and bond breaking behaviors of molecules. In this study, we extend the CMR method to the treatment of electron correlations in periodic solid systems. Using a linear hydrogen chain as a benchmark system, we show that the results from the CMR method compare very well with those obtained recently by accurate quantum Monte Carlo (QMC) calculations. We also study the equation of states of three-dimensional crystalline phases of atomic hydrogen. We show that the results from the CMR method agree much better with the available QMC data in comparison with those from density functional theory and Hartree-Fock calculations.
Abstract An appropriate treatment of electronic correlation effects plays an important role in accurate descriptions of physical and chemical properties of real materials. The recently proposed correlation matrix renormalization theory with sum rule correction (CMR) [1] for studying correlated-electron materials has shown good performance in molecular systems and a periodic hydrogen chain in comparison with various quantum chemistry and quantum Monte Carlo calculations [2]. This work gives a detailed formulation and computational code implementation of CMR in multi-band periodic lattice systems. This lattice CMR ab initio theory is highly efficient, has no material specific adjustable parameters, and has no double counting issues faced by the hybrid approaches like LDA + U , DFT + DMFT and DFT + GA type theories. Benchmark studies on materials with s and p orbitals in this study show that CMR in its current implementation consistently performs well for these systems as the electron correlation increases from the bonding region to the bond breaking region.
A variety of quantum many-body methods have been developed for studying the strongly correlated electron systems. We have also proposed a computationally efficient and accurate approach, named the correlation matrix renormalization (CMR) method to address the challenges. The theoretic development and benchmark tests of the CMR method are included in this thesis. Meanwhile, ground state total energy is the most important property of electronic calculations. We also investigated an alternative approach to calculate the total energy, and extended this method for magnetic anisotropy energy of ferromagnetic materials. In addition, another theoretical tool, dynamical mean-field theory on top of the density functional theory, has also been used in electronic structure calculations for an Iridium oxide to study the phase transition, which results from an interplay of the d electrons' internal degrees of freedom.
We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.
We present an efficient method for calculating the electronic structure and total energy of strongly correlated electron systems. The method extends the traditional Gutzwiller approximation for one-particle operators to the evaluation of the expectation values of two particle operators in the many-electron Hamiltonian. The method is free of adjustable Coulomb parameters, and has no double counting issues in the calculation of total energy, and has the correct atomic limit. We demonstrate that the method describes well the bonding and dissociation behaviors of the hydrogen and nitrogen clusters, as well as the ammonia composed of hydrogen and nitrogen atoms. We also show that the method can satisfactorily tackle great challenging problems faced by the density functional theory recently discussed in the literature. The computational workload of our method is similar to the Hartree-Fock approach while the results are comparable to high-level quantum chemistry calculations.
Describing correlated electron systems has been a major challenge in computational condensed-matter physics. Quantum Monte Carlo, a powerful computational tool for the study of correlated systems, solves electron correlation problems explicitly. It has been taken as a benchmark method for understanding the correlated systems. Instead of making approximations to Hamiltonian, QMC methods work with the wave functions, and the computational cost scales well with the system size. With the development of parallel computing, QMC calculations on large systems are becoming more and more feasible. We have investigated two correlated systems with highly accurate fixed node QMC techniques. The first system is a correlated hydrogen model system near the metal to insulator transition. We have successfully identified the transition point by calculating spin and charge properties and analyzing the low energy Hilbert space. The second one is a strongly correlated Fe/O system. Calculations on the Fe atoms, O atoms, and FeO molecules are conducted with multiple highly accurate many-body techniques. The source of errors has been disentangled by comparing the results of the many body techniques with the experimental results. For the Fe and O atoms, the calculated properties coincide well with previous experimental results. For the basis-based techniques, the performance is mainly limited by the basis set. The calculated equilibrium bond length, excitation energy and vibrational frequency of the FeO molecules are also in close agreement with the known values from previous experiments.
In this paper, we report a fully ab initio variational Monte Carlo study of the linear and periodic chain of hydrogen atoms, a prototype system providing the simplest example of strong electronic correlation in low dimensions. In particular, we prove that numerical accuracy comparable to that of benchmark density-matrix renormalization-group calculations can be achieved by using a highly correlated Jastrow-antisymmetrized geminal power variational wave function. Furthermore, by using the so-called ``modern theory of polarization'' and by studying the spin-spin and dimer-dimer correlations functions, we have characterized in detail the crossover between the weakly and strongly correlated regimes of this atomic chain. Our results show that variational Monte Carlo provides an accurate and flexible alternative to highly correlated methods of quantum chemistry which, at variance with these methods, can be also applied to a strongly correlated solid in low dimensions close to a crossover or a phase transition.