Ground and excited states of even-numbered Hubbard ring at half-filling: comparison of the extended Gutzwiller approach with exact diagonalization

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2023-03-27
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Fang, Yimei
Zhang, Feng
Ye, Zhuo
Zhang, Han
Lu, Wen-Cai
Wu, Shunqing
Yao, Yong-Xin
Wang, Cai-Zhuang
Ho, Kai-Ming
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Iowa State University Digital Repository, Ames IA (United States)
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Ames National Laboratory

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It remains a great challenge in condensed matter physics to develop a method to treat strongly correlated many-body systems with balanced accuracy and efficiency. We introduce an extended Gutzwiller (EG) method incorporating a manifold technique, which builds an effective manifold of the many-body Hilbert space, to describe the ground-state (GS) and excited-state (ES) properties of strongly correlated electrons. We systematically apply an EG projector onto the GS and ES of a non-interacting system. Diagonalization of the true Hamiltonian within the manifold formed by the resulting EG wavefunctions gives the approximate GS and ES of the correlated system. To validate this technique, we implement it on even-numbered fermionic Hubbard rings at half-filling with periodic boundary conditions, and compare the results with the exact diagonalization (ED) method. The EG method is capable of generating high-quality GS and low-lying ES wavefunctions, as evidenced by the high overlaps of wavefunctions between the EG and ED methods. Favorable comparisons are also achieved for other quantities including the total energy, the double occupancy, the total spin and the staggered magnetization. With the capability of accessing the ESs, the EG method can capture the essential features of the one-electron removal spectral function that contains contributions from states deep in the excited spectrum. Finally, we provide an outlook on the application of this method on large extended systems.
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This is a manuscript of an article published as Fang, Yimei, Feng Zhang, Zhuo Ye, Han Zhang, Wen-Cai Lu, Shunqing Wu, Yong-Xin Yao, Cai-Zhuang Wang, and Kai-Ming Ho. "Ground and excited states of even-numbered Hubbard ring at half-filling: comparison of the extended Gutzwiller approach with exact diagonalization." Journal of Physics: Condensed Matter 35, no. 26 (2023): 265602. DOI: 10.1088/1361-648X/acc7ed. Copyright 2023 IOP Publishing Ltd. Posted with permission. DOE Contract Number(s): AC02-07CH11358; 12147138; 11874307; 20720210023; 21773132
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