Quantum Lifshitz Point in the Infinite-Dimensional Hubbard Model

We show that the Gutzwiller variational wave function is very accurate for the computation of magnetic phase boundaries in the infinite-dimensional Hubbard model. This allows us to substantially extend known phase diagrams. For both the half-hypercubic and the hypercubic lattice, a large part of the phase diagram is occupied by an incommensurate phase, intermediate between the ferromagnetic and the paramagnetic phase. In case of the hypercubic lattice, the three phases join at a new quantum Lifshitz point at which the order parameter is critical and the stiffness vanishes.

Figure 1

Magnon dispersions for the (fully polarized) ferromagnet in the half-hypercubic lattice for $\delta =0.3$. At this doping the FM solution is stable for $U>0.49U_{\mathrm{BR}}$.

Figure 2

Full line: limit of stability of the FM phase within the Gutzwiller wave function for the hhc lattice. The asterisks are the exact result from Ref. 16. In the inset, a scaled representation of the FM stability limit is shown with $U_{\mathrm{red}}=U/(U+U_{\mathrm{BR}})$ and $U_{\mathrm{BR}}=6.86t$. Dashed line: limit of stability of the PM phase. The arrows indicate the value of ${\eta }_{\mathbf{q}}$ parametrizing the momentum of the unstable mode.

Figure 3

Limit of stability of the FM (full line) and PM (dashed line) phases for the hc lattice. Arrows indicate the value of ${\eta }_{\mathbf{q}}$ for the unstable mode of the PM phase. The stars correspond to the limit of stability of the FM phase obtained in Ref. 24 within an approximate solution of the DMFT equations. Dotted lines are levels of constant magnetization. Energies are in units of $U_{\mathrm{BR}}=6.38t$.