Bond-dependent slave-particle cluster theory

General and exact solutions of large, strongly-correlated electron problems, exemplified by the Hubbard model on a lattice, are challenging. A wide variety of approaches exist in the field, and recent occupation-number based slave-particle methods [1-4] represent a computationally efficient approach.  Here, one decoupling the electronic spin and charge degrees of freedoms to end up with a non-interacting fermion problem on the lattice and an interacting auxiliary slave problem on the lattice.  One must then truncate or simplify the slave problem to render it tractable.

In this work, we introduce a new cluster slave-particle theory, for Hubbard models describing transition metal oxides, based on the expansion of the ground-state 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 Mott transition in one dimension). We test our approach on 1D and 2D dp model systems and compare to numerically exact results based on density matrix renormalization group (DMRG).  We find that our approach is computationally economical and reproduces good total energy, site occupancy, double occupancy and spin correlations. 

References

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[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)