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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 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. Disciplines Condensed Matter Physics | Physics This article is available at Iowa State University Digital Repository: https://lib.dr.iastate.edu/ameslab_manuscripts/127 PHYSICAL REVIEW B 97, 075142 (2018) Correlation matrix renormalization theory for correlated-electron materials with application to the crystalline phases of atomic hydrogen Xin Zhao, Jun Liu,* Yong-Xin Yao, Cai-Zhuang Wang, and Kai-Ming Ho Ames Laboratory, U.S. DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA (Received 2 November 2017; revised manuscript received 23 January 2018; published 23 February 2018) 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