2022 Workshop on Recent Developments in Electronic Structure (ES22) Poster Session

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Author: Jin, Zheting, Yale University

Title: Bond-dependent slave-particle cluster theory based on density matrix expansion

Abstract: Solving large and strongly-correlated electronic problems, exemplified by the Hubbard model on a lattice, is an ongoing electronic structure challenge, and a wide variety of approaches exist in the field. Recent occupation-number based slave-particle methods [1-4] represent a computationally efficient approach for obtaining approximation solutions.  In these methods, one decouples the electronic spin and charge degrees of freedom to end up with an easy non-interacting fermion problem on the lattice and an easier interacting auxiliary slave problem on the lattice.  However, one must then truncate or simplify the slave problem to render it tractable computationally.

We introduce a new cluster slave-particle method for Hubbard models describing transition metal oxides.  The method is based on the expansion of the lattice density matrix into a set of overlapping clusters in real space.  Our approach includes all the nearest-neighbor hopping terms directly within the interacting clusters and does not truncate or approximate them at cluster boundaries (unlike prior cluster approaches including cluster DMFT [5-7]).  The approach also overcomes some of the shortcomings of prior single-site slave-particle methods (e.g., predicting a false Mott transition in one dimension). We test our approach on 1D and 2D p-d model systems and compare to numerically exact results based on exact diagonalization and density matrix renormalization group (DMRG).  We find that our approach is computationally economical and high-quality total energies, site occupancies and d-site double occupancies as a function of Coulomb interaction strength and doping.

[1] S. Florens and A. Georges, Phys. Rev. B 70, 035114 (2004)
[2] L. de’Medici, A. Georges, and S. Bierman, Phys. Rev. B 72, 205124 (2005)
[3] B. Lau and A. Millis, Phys. Rev. Letter 110, 126404 (2013)
[4] A. Georgescu and S. Ismail-Beigi, Phys. Rev. B 92, 235117 (2015)
[5] S. Hassan and L. de’Medici, Phys. Rev. B 81, 035106 (2010)
[6] E. Zhao and A. Paramekanti, Phys. Rev. B 76, 195101 (2007)
[7] M. Hettler et al., Phys. Rev. B 58, 7475 (1998)

Other authors: Ismail-Beigi, Sohrab, Yale University


Bond-dependent slave-particle cluster theory based on density matrix expansion