Bosonic Mott Insulator with Meissner Currents

We introduce a generic bosonic model exemplifying that (spin) Meissner currents can persist in insulating phases of matter. We consider two species of interacting bosons on a lattice. Our model exhibits separation of charge (total density) and spin (relative density): the charge sector is gapped in a bosonic Mott insulator phase with total density one, while the spin sector remains superfluid due to interspecies conversion. Coupling the spin sector to the gauge fields yields a spin Meissner effect reflecting the long-range spin superfluid coherence. We investigate the resulting phase diagram and describe other possible spin phases of matter in the Mott regime possessing chiral currents as well as a spin-density wave phase. The model presented here is realizable in Josephson junction arrays and in cold atom experiments.

Figure 1

Phase diagram for the effective gauged spin-$\frac{1}{2}$ model in Eq. (5) built for large repulsive terms $U$ and $V_{\perp }$. In the $XY$ limit, depending on flux, there is a spin Meissner phase or a vortex lattice phase (the direction of current patterns is shown in each phase). The inset shows the Mott lobe with total density $\rho =1$ of interest, obtained using the density matrix renormalization group method for the one-dimensional model. The dashed line is the mean-field theory result.