Spin density waves in the Hubbard model: A DMFT approach

We analyze spin density waves (SDWs) in the Hubbard model on a square lattice within the framework of inhomogeneous dynamical mean field theory (IDMFT). Doping the half-filled Hubbard model results in a change of the antiferromagnetic Néel state, which exists exactly at half filling, to a phase of incommensurate SDWs. Previous studies of this phase mainly rely on static mean field calculations. In this paper, we will use large-scale IDMFT calculations to study properties of SDWs in the Hubbard model. A great advantage of IDMFT over static mean field approaches is the inclusion of local screening effects and the easy access to dynamical correlation functions. Furthermore, this technique is not restricted to the Hubbard model, but can be easily used to study incommensurate phases in various strongly correlated materials.

Figure 1

Typical pattern for a vertical SDW state in the Hubbard model for $U=8t$ and an average electron density $\langle n\rangle =0.9$. The upper (lower) panel shows the electron polarization (density).

Figure 2

Phase diagram of the Hubbard on a square lattice as calculated by IDMFT. The shaded region represents parameters where we find vertical as well as diagonal SDWs to be stable. The homogeneous Néel state exists exactly at half filling for all interaction strengths and for a slightly doped region at weak interaction.

Figure 3

(a) Electron density against lattice sites for different average electron densities and $U=8t$. We only show a single oscillation of the electron density which is periodically continued. (b) The extracted period of the modulation of the electron density against the reciprocal density of holes, $1/(1-n)$ ($n$ is the average number of electrons per lattice site). (c) Electron density against lattice sites for different interaction strengths and fixed average electron density $n=0.9$. (d) The magnitude of the spin polarization, $P=|n_{\uparrow }-n_{\downarrow }|$, against different lattice sites for different interaction strengths.

Figure 4

Left: Occupation number of different lattice sites of a vertical SDW for a fixed chemical potential and interaction strength but different cluster sizes. Right: Direct comparison of a single period of the SDW for different cluster sizes. (The colors of the right panel correspond to the colors of the left panels.)

Figure 5

Momentum-resolved spectral function for the half-filled Hubbard model for $U=8t$. The green line marks the Fermi energy.

Figure 6

Momentum-resolved spectral function for the doped Hubbard model for $U=8t$, $\langle n\rangle =0.95$ in the vertical SDW state. The green line marks the Fermi energy. The lower panel is a magnification around the Fermi energy.

Figure 7

Momentum-resolved spectral function for the doped Hubbard model for $U=8t$, $\langle n\rangle =0.95$ in the square-lattice-symmetric SDW state. The green line marks the Fermi energy.