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Physical review. B, Condensed matter

Density of hole states for the strongly correlated infinite-dimensional Hubbard model

Sam Y. S. Yang

Published Aug 1, 1992• 3 citations
Publisher

Abstract

The density of hole states for the strongly correlated infinite-dimensional Hubbard model is studied with use of the moment-expansion method. While exact results suggest a divergent spectrum width for ferromagnetic spin configurations, numerical calculations indicate a finite spectrum width for antiferromagnetic and random spin configurations. The spectrum widths for antiferromagnetic and random spin configurations are 5.6568\ifmmode\pm\else\textpm\fi{}0.0001 and 10\ifmmode\pm\else\textpm\fi{}2, respectively.

DOI
10.1103/physrevb.46.3120

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The density of hole states for the strongly correlated infinite-dimensional Hubbard model is studied with use of the moment-expansion method. While exact results suggest a divergent spectrum width for ferromagnetic spin configurations, numerical calculations indicate a finite spectrum width for antiferromagnetic and random spin configurations. The spectrum widths for antiferromagnetic and random spin configurations are 5.6568\ifmmode\pm\else\textpm\fi{}0.0001 and 10\ifmmode\pm\else\textpm\fi{}2, respectively.
The density of hole states for the strongly correlated nearly-half-filled Hubbard model on d-dimensional hypercubic lattices is studied using the moment-expansion method of Brinkman and Rice. Analysis of the extended series suggests that the density of hole states, for antiferromagnetic and random electron spin configurations, has an essential singularity inside the ferromagnetic band edges for d=2, 3, 4, and 5 with characteristic exponents 0.50 and 0.39, respectively. In all cases there is a distinctive narrowing of the spectrum, which becomes more pronounced for larger d. For the dimensionalities studied, the antiferromagnetic case gave the narrowest spectra.
The effective Hamiltonian, obtained from the Hubbard model in the strong-coupling limit, is diagonalized exactly for a periodic two-dimensional square lattice of ten sites. We obtain the ground state of the system for any filling of the lattice and the KKK-space excitation spectrum for a single hole. Within our finite-size system, it is found that for very small coupling ratio tU\frac{t}{U}Ut​, each hole creates a local ferromagnetic environment at least of the size of our system, whereas for increasing tU\frac{t}{U}Ut​, the holes tend to form clusters, induced by antiferromagnetic spin correlations. A range of tU\frac{t}{U}Ut​ exists for which pairing of the holes may be possible.
We present different numerical calculations based on variational quantum Monte Carlo simulations supporting a ferromagnetic ground state for finite and small hole densities in the two-dimensional infinite-U Hubbard model. Moreover, by studying the energies of different total spin sectors, these calculations strongly suggest that the paramagnetic phase is unstable against a phase with a partial polarization for large hole densities delta approximately 0.40 with evidence for a second-order transition to the paramagnetic large doping phase.
The infinite-U Hubbard model on finite two-dimensional square lattices is investigated by the use of exact numerical diagonalization. Configurations with one spin flip away from the ferromagnetic state and up to three holes are studied for lattice sizes ranging from 4*4 to 12*12. For all these situations, the state with one spin flip is found to be more stable than the Nagaoka ferromagnetic state. The crystal momentum of the ground state in this spin sector depends on the system size. Systematic comparison with the Gutzwiller wavefunction shows that it reproduces qualitatively the crystal momentum dependence of the energy, but not the exact correlation between the spin flip and the holes.
Two-dimensional Hubbard lattices with two or three holes are investigated as a function of UUU in the large-UUU limit. In the so-called Nagaoka limit (one-hole system at infinite UUU), it is known that the Hubbard model exhibits a ferromagnetic ground state. Here, by means of exact full configuration interaction quantum Monte Carlo simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing UUU. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centered on individual holes. The overall total spin of the wave functions remains the lowest possible (0 or 12\frac{1}{2}21​, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than 1) number of holes.