Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model

Details Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model

2011-07-05

arxiv.org/abs/1107.0976v3

J. Phys.: Condens. Matter 23 (2011) 505601

Physics

Condensed Matter

Strongly Correlated Electrons

13 pages, 17 figure, 0 tables

Scientific paper

10.1088/0953-8984/23/50/505601

The ground states of the two-dimensional repulsive Hubbard model are studied within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge properties are determined by systematic, large-scale, exact numerical calculations, and quantified as a function of electron doping $h$. In the solution of the self-consistent UHF equations, multiple initial configurations and simulated annealing are used to facilitate convergence to the global minimum. New approaches are employed to minimize finite-size effects in order to reach the thermodynamic limit. At low to moderate interacting strengths and low doping, the UHF ground state is a linear spin-density wave (l-SDW), with antiferromagnetic order and a modulating wave. The wavelength of the modulating wave is $2/h$. Corresponding charge order exists but is substantially weaker than the spin order, hence holes are mobile. As the interaction is increased, the l-SDW states evolves into several different phases, with the holes eventually becoming localized. A simple pairing model is presented with analytic calculations for low interaction strength and small doping, to help understand the numerical results and provide a physical picture for the properties of the SDW ground state. By comparison with recent many-body calculations, it is shown that, for intermediate interactions, the UHF solution provides a good description of the magnetic correlations in the true ground state of the Hubbard model.

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