Figure 1

Diagram corresponding to perturbation orders $m_F=1$, $m_K=1$, $m_{K^{*}}=1$, $m_{\varphi }=2$, $m_{{\varphi }^{*}}=2$, and $n(\tau =0)=2$.Reuse & Permissions

Figure 2

Top panel: Phase diagram (superfluid to normal liquid transition) in the space of interaction and temperature for $n=1$. The dashed line shows the static mean field result, the red curve the exact solution for a Bethe lattice with coordination number $z=6$ (Ref. 20), and the blue curve with open diamonds the QMC result from lattice simulations (Ref. 12). The black line with open circles corresponds to the B-DMFT solution, which yields a second-order transition. Bottom panel: Ground-state phase diagram in the space of $t/U$ and $\mu /U$, showing the first two Mott lobes surrounded by superfluid. The B-DMFT phase boundary was computed at $\beta t=2$. Error bars are much smaller than the symbol size.Reuse & Permissions

Figure 3

Comparison of the connected density-density correlation functions $⟨n(\tau )n(0)⟩-⟨n{⟩}^2$ in the normal ($U=20$, $\mu =8.72$, $\beta =0.2$), superfluid ($U=10$, $\mu =0.7$, $\beta =2$), and Mott insulating ($U=40$, $\mu =11$, $\beta =2$) phases. The left panel shows the B-DMFT result and the right panel the exact data from lattice QMC calculations. The data for the Mott phase are scaled by a factor 10.Reuse & Permissions