Phase diagram of one-dimensional hard-core bosons with three-body interactions

We determine the phase diagram of a one-dimensional system of hard-core lattice bosons interacting via repulsive three-body interactions by analytic methods and extensive quantum Monte Carlo simulations. Such three-body interactions can be derived from a microscopic theory for polar molecules trapped in an optical lattice. Depending on the strength of the interactions and the particle density, we find superfluid and solid phases, the latter appearing at an unconventional filling of the lattice and displaying a coexistence of charge-density wave and bond orders.

Figure 1

(Color online) (QMC method: WA) Phase diagram of hard-core lattice bosons with dominant three-body interactions [Eq. (1)] in the grand-canonical ensemble, $\mu /W$ vs $J/W$. The solid phase at filling $n=2/3$ is characterized by a coexistence of CDW and BOW orders.

Figure 2

(Color online) (QMC method: SSE) Lattice filling $n=2/3$. (a) Bond-order structure factor $S_{\text{BOW}}\left(2\pi /3\right)/L$ vs $W/J$. Top to bottom: lattice sizes $L=36$, 60, 120, 240, and 300; the TDL is indicated. Dashed line: strong-coupling perturbative result $4/9{\left(J/W\right)}^2$. (b) Density structure factor $S_{\text{CDW}}\left(2\pi /3\right)/L$ vs $W/J$. Top to bottom: lattice sizes $L=36$, 60, 120, 240, and 300; the TDL is indicated. Dashed line: strong-coupling result $n^2/4=1/9$. (c) Superfluid density ${\rho }_s$ as a function of $W/J$ for lattice sizes $L=36$, 60, and 120. Inset: $W_c/J$ as a function of $1/{\text{ln}}^{2}L$ results from the WA. The line is a guide for the eyes.

Figure 3

(Color online) (QMC method: WA) Lattice filling $n=1/2$. (a) Luttinger liquid parameter $K$ as a function of $W/J$ with critical value $K_c=0.5$ (dashed line) of the superfluid to solid transition. The inset shows the density structure factor $S_{\text{CDW}}\left(\pi \right)/L$ as a function of the inverse system size $1/L$ for $W/J=1000$. (b) Phase diagram in the presence of an additional nearest-neighbor interaction $V_1$ in the plane $W/J$ vs $V_1/J$. The arrow indicates the point of the superfluid to solid transition at $W/J=0$.

Figure 4

(QMC method: SSE) Superfluid fraction ${\rho }_s$ as a function of $W/J$ for fillings $n=1/3$, 1/2, and 2/3. Gray and black lines correspond to system sizes $L=60$ and 120, respectively. Due to particle-hole symmetry, the superfluid fractions for $n=1/3$ and 2/3 are the same for $W/J=0$.