1
|
Ye Z, Zhang F, Fang Y, Zhang H, Wu S, Lu WC, Yao YX, Wang CZ, Ho KM. A rotationally invariant approach based on Gutzwiller wave function for correlated electron systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:495601. [PMID: 36220012 DOI: 10.1088/1361-648x/ac9945] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2022] [Accepted: 10/11/2022] [Indexed: 06/16/2023]
Abstract
We introduce a rotationally invariant approach combined with the Gutzwiller conjugate gradient minimization method to study correlated electron systems. In the approach, the Gutzwiller projector is parametrized based on the number of electrons occupying the onsite orbitals instead of the onsite configurations. The approach efficiently groups the onsite orbitals according to their symmetry and greatly reduces the computational complexity, which yields a speedup of20∼50×in the minimal basis energy calculation of dimers. The computationally efficient approach promotes more accurate calculations beyond the minimal basis that is inapplicable in the original approach. A large-basis energy calculation of F2demonstrates favorable agreements with standard quantum-chemical calculations Bytautaset al(2007J. Chem. Phys.127164317).
Collapse
Affiliation(s)
- Zhuo Ye
- Ames Laboratory-US DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, United States of America
| | - Feng Zhang
- Ames Laboratory-US DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, United States of America
| | - Yimei Fang
- Department of Physics, OSED, Key Laboratory of Low Dimensional Condensed Matter Physics Department of Education of Fujian Province Jiujiang Research Institute, Xiamen University, Xiamen 361005, People's Republic of China
| | - Han Zhang
- College of Physics, Qingdao University, Qingdao, Shandong 266071, People's Republic of China
| | - Shunqing Wu
- Department of Physics, OSED, Key Laboratory of Low Dimensional Condensed Matter Physics Department of Education of Fujian Province Jiujiang Research Institute, Xiamen University, Xiamen 361005, People's Republic of China
| | - Wen-Cai Lu
- College of Physics, Qingdao University, Qingdao, Shandong 266071, People's Republic of China
| | - Yong-Xin Yao
- Ames Laboratory-US DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, United States of America
| | - Cai-Zhuang Wang
- Ames Laboratory-US DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, United States of America
| | - Kai-Ming Ho
- Ames Laboratory-US DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, United States of America
| |
Collapse
|
2
|
Ye Z, Fang Y, Zhang H, Zhang F, Wu S, Lu WC, Yao YX, Wang CZ, Ho KM. The Gutzwiller conjugate gradient minimization method for correlated electron systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:243001. [PMID: 35290968 DOI: 10.1088/1361-648x/ac5e03] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2021] [Accepted: 03/15/2022] [Indexed: 06/14/2023]
Abstract
We review our recent work on the Gutzwiller conjugate gradient minimization method, anab initioapproach developed for correlated electron systems. The complete formalism has been outlined that allows for a systematic understanding of the method, followed by a discussion of benchmark studies of dimers, one- and two-dimensional single-band Hubbard models. In the end, we present some preliminary results of multi-band Hubbard models and large-basis calculations of F2to illustrate our efforts to further reduce the computational complexity.
Collapse
Affiliation(s)
- Zhuo Ye
- Ames Laboratory-US DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, United States of America
| | - Yimei Fang
- Department of Physics, OSED, Key Laboratory of Low Dimensional Condensed Matter Physics, (Department of Education of Fujian Province) Jiujiang Research Institute, Xiamen University, Xiamen 361005, People's Republic of China
| | - Han Zhang
- College of Physics, Qingdao University, Qingdao, Shandong 266071, People's Republic of China
| | - Feng Zhang
- Ames Laboratory-US DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, United States of America
| | - Shunqing Wu
- Department of Physics, OSED, Key Laboratory of Low Dimensional Condensed Matter Physics, (Department of Education of Fujian Province) Jiujiang Research Institute, Xiamen University, Xiamen 361005, People's Republic of China
| | - Wen-Cai Lu
- College of Physics, Qingdao University, Qingdao, Shandong 266071, People's Republic of China
| | - Yong-Xin Yao
- Ames Laboratory-US DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, United States of America
| | - Cai-Zhuang Wang
- Ames Laboratory-US DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, United States of America
| | - Kai-Ming Ho
- Ames Laboratory-US DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, United States of America
| |
Collapse
|
3
|
Liu J, Zhao X, Yao Y, Wang CZ, Ho KM. Correlation matrix renormalization theory in multi-band lattice systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 33:095902. [PMID: 33017810 DOI: 10.1088/1361-648x/abbe78] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Accepted: 10/05/2020] [Indexed: 06/11/2023]
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 CMRab initiotheory 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.
Collapse
Affiliation(s)
- Jun Liu
- Ames Laboratory-U.S. DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, United States of America
| | - Xin Zhao
- Ames Laboratory-U.S. DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, United States of America
| | - Yongxin Yao
- Ames Laboratory-U.S. DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, United States of America
| | - Cai-Zhuang Wang
- Ames Laboratory-U.S. DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, United States of America
| | - Kai-Ming Ho
- Ames Laboratory-U.S. DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, United States of America
| |
Collapse
|
4
|
A benchmark of Gutzwiller conjugate gradient minimization method in ground state energy calculations of dimers. COMPUT THEOR CHEM 2020. [DOI: 10.1016/j.comptc.2020.112877] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
|
5
|
Ye Z, Yao YX, Wang CZ, Ho KM. First-principles calculation of excited states of diatomic molecules: a benchmark for the Gutzwiller conjugate gradient minimisation method. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1734243] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Zhuo Ye
- Ames Laboratory – US DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA, USA
| | - Yong-Xin Yao
- Ames Laboratory – US DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA, USA
| | - Cai-Zhuang Wang
- Ames Laboratory – US DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA, USA
| | - Kai-Ming Ho
- Ames Laboratory – US DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA, USA
- Hefei National Laboratory for Physical Sciences at Microscale, International Center for Quantum Design of Functional Materials (ICQD) and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, People’s Republic of China
| |
Collapse
|
6
|
Ye Z, Yao YX, Zhao X, Wang CZ, Ho KM. First-principles calculation of correlated electron materials based on Gutzwiller wave function beyond Gutzwiller approximation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:335601. [PMID: 31067512 DOI: 10.1088/1361-648x/ab2032] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We propose an approach that is under the framework of Gutzwiller wave function but goes beyond the commonly adopted Gutzwiller approximation to improve the accuracy and flexibility in treating the correlation effects. Detailed formalism is described for a dimer which is straightforwardly generalized later to more complicated periodic bulk systems. The accuracy of the approach is demonstrated by evaluating the potential energy curves of spin-singlet N2 dimer, spin-triplet O2 dimer, and 1D hydrogen chain. The computational workload of the approach can be easily handled by efficient parallel computing.
Collapse
Affiliation(s)
- Zhuo Ye
- Ames Laboratory-US DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, United States of America
| | | | | | | | | |
Collapse
|
7
|
Zhang H, Lu WC, Yao YX, Wang CZ, Ho KM. Benchmark of correlation matrix renormalization method in molecule calculations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:195902. [PMID: 30736027 DOI: 10.1088/1361-648x/ab05b3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We report benchmark calculations of the correlation matrix renormalization (CMR) approach for 23 molecules in the well-established G2 molecule set. This subset represents molecules with spin-singlet ground state in a variety of chemical bonding and coordination environments. The QUAsi-atomic minimal basis-set orbitals (QUAMBOs) are used as local orbitals in both CMR and full configuration interaction (FCI) calculations for comparison. The results obtained from the calculations are also compared with available experimental data. It is shown that the CMR method produces binding and dissociation energy curves in good agreement with the QUAMBO-FCI calculations as well as experimental results. The CMR benchmark calculations yield a standard deviation of 0.09 Å for the equilibrium bond length and 0.018 Hartree/atom for the formation energy, with a gain of great computational efficiency which scales like Hartree-Fock method.
Collapse
Affiliation(s)
- Han Zhang
- College of Physics and State Key Laboratory of Bio-Fibers and Eco-Textiles, Qingdao University, Shandong 266071, People's Republic of China
| | | | | | | | | |
Collapse
|
8
|
Bytautas L, Dukelsky J. Seniority based energy renormalization group (Ω-ERG) approach in quantum chemistry: Initial formulation and application to potential energy surfaces. COMPUT THEOR CHEM 2018. [DOI: 10.1016/j.comptc.2018.08.011] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
|