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arXiv · 1107.0976

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

Jie Xu·Chia-Chen Chang·Eric J. Walter·Shiwei Zhang
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Abstract

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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Jie Xu, Chia-Chen Chang, Eric J. Walter, Shiwei Zhang. 2011-12-01. Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model. https://doi.org/10.1088/0953-8984%2F23%2F50%2F505601

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