Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model

We analyze the quantum phase transition in the Bose-Hubbard model borrowing two tools from quantum-information theory, i.e., the ground-state fidelity and entanglement measures. We consider systems at unitary filling comprising up to 50 sites and show for the first time that a finite-size scaling analysis of these quantities provides excellent estimates for the quantum critical point. We conclude that fidelity is particularly suited for revealing a quantum phase transition and pinning down the critical point thereof, while the success of entanglement measures depends on the mechanisms governing the transition.

Figure 1

Mott lobe at filling $\nu =1$. Different colors correspond to different sizes as specified by the color code. The dot signals the critical point at filling $\nu =1$. Note that finite-size effects prevent the collapse of the critical boundaries.

Figure 2

Extrema of $\mathcal{F}$ and $\mathcal{S}$. The vertical stripe and line signal $J_{\infty }$ as reported in Refs. 20, 27, 28.

Figure 3

Extrema of $\mathcal{E}$ and its derivatives. The vertical stripes and lines signal $J_{\infty }$ as in Fig. 2.

Figure 4

Finite-size scaling of the extrema (dots) in the considered quantities. Solid and dashed lines denote the fits and the relevant estimates of $J_{\infty }$, as specified by the color code. The entanglement in the ring (CCG) is evaluated with respect to QM (SM). The known values of $J_{\infty }$ are included as well.

Figure 5

Contour plot of $\mathcal{S}(\mu ,J)$ for the ground state of the mean-field Hamiltonian (2).