Phase boundary of the boson Mott insulator in a rotating optical lattice

We consider the Bose-Hubbard model in a two-dimensional rotating optical lattice and investigate the consequences of the effective magnetic field created by rotation. Using a Gutzwiller-type variational wave function, we find an analytical expression for the Mott insulator (MI)–superfluid (SF) transition boundary in terms of the maximum eigenvalue of the Hofstadter butterfly. The dependence of phase boundary on the effective magnetic field is complex, reflecting the self-similar properties of the single particle energy spectrum. Finally, we argue that fractional quantum Hall phases exist close to the MI-SF transition boundaries, including MI states with particle densities greater than one.

Figure 1

(Color online) Maximum energy of the Hofstadter butterfly $f\left(\varphi \right)$ for a given $\varphi =p∕q$. This value is calculated as the maximum eigenvalue of the matrix ${\mathbb{A}}_q={\mathbb{A}}_q\left(k_x=0,k_y=0\right)$ [Eq. (2)].

Figure 2

(Color online) The boundary of the Mott insulator phase for the first three Mott lobes. The figure is periodic in $\varphi$. Magnetic field increases the critical value for $t∕U$, as expected; however, this increase is not monotonic. Transition boundary for two different values of $\mu ∕U$ are marked to display the complex structure of the surface.

Figure 3

Schematic phase diagram near the $n_0$th Mott lobe. Dotted lines show the chemical potential as a function of hopping strength for systems with constant density $⟨\widehat{n}⟩=n_0$ and $⟨\widehat{n}⟩=n_0+\epsilon$. FQH phases of “excess” particles or holes are shown as the shaded regions.