Anyon Hubbard Model in One-Dimensional Optical Lattices

Raman-assisted hopping may be used to realize the anyon Hubbard model in one-dimensional optical lattices. We propose a feasible scenario that significantly improves the proposal of T. Keilmann et al. [Nat. Commun. 2, 361 (2011)], allowing as well for an exact realization of the two-body hard-core constraint, and for controllable effective interactions without the need of Feshbach resonances. We show that the combination of anyonic statistics and two-body hard-core constraint leads to a rich ground-state physics, including Mott insulators with attractive interactions, pair superfluids, dimer phases, and multicritical points. Moreover, the anyonic statistics results in a novel two-component superfluid of holon and doublon dimers, characterized by a large but finite compressibility and a multipeaked momentum distribution, which may be easily revealed experimentally.

Figure 1

(a) Raman scheme proposed for the realization of the AHM. (b) Raman-assisted hops (i)–(iv) discussed in the text.

Figure 2

Phase diagram of the AHM: (a) dilute limit ($\rho \to 0$), (b) incommensurate intermediate fillings (here $\rho =1/2$), and (c) unit filling ($\rho =1$). The PSF-SF transition lines [boxes or solid line in (a)], extracted from the crossing of two and one particle excitations coincides with the onset of parity order. At incommensurate fillings for small $\varphi$, the system exhibits a first order transition from the SF to PSF phase through a forbidden region (FR) (dotted area). For $\varphi /\pi \gtrsim 0.6$ we find the PP phase. For unit filling the Ising-type PSF-SF transition and the Kosterlitz-Thouless SF-MI transition lines cross around $\varphi /\pi \approx 0.8$ in a multicritical point. For larger values of $\varphi$ the system exhibits a dimerized gapped phase D. (d) Grand-canonical phase diagram and lines of constant density $\rho$ for $U=0$ as a function of $\mu$ and $\varphi$. Solid lines denote the MI and PP phase; the rest is SF. For $\mu /t<-2$ ($\mu /t>4$), the vacuum $\rho =0$ (fully occupied phase, $\rho =2$) is realized.

Figure 3

Phase transitions for $\varphi =\pi$. (a) Equation of state, density $\rho$ as function of chemical potential $\mu$ (calculated for $L=48$ sites, $U=0$). The inset shows a detailed view on the PP region for $L=240$ sites. (b) Estimation of the central charge for $L=24$ (dashed line) and $L=48$ (solid line) sites and periodic boundary conditions ($\rho =1/2$). The inset shows fits to the block-entanglement entropy $S_{vN}$ for (from bottom to top) $U=2,-2,-1.0$. (c) Sum of local single-($N_a$) and two-particle correlations ($N_d$) for $L=60$ sites and $\rho =1/2$, see text.

Figure 4

(a) Quasimomentum distribution $n(k)$ for $\rho =1/2$ as a function of $U/t$ for $\varphi =0.9\pi$ ($L=60$ sites). Dashed lines denote phase transitions between PSF, PP, and SF phases. (b) and (c) show the momentum distribution for $U=2t$ and $U=0$ for the AHM (solid line) and the components $A$ (dashed line) and $B$ (dotted line) separately (for bosonic atoms). The latter are obtained by direct simulation of the two-component model with Raman-induced hopping (see the Supplemental Material [32] for a discussion of the fermionic case).