Possible Exciton Bose Liquid in a Hard-Core Boson Ring Model

We present a quantum Monte Carlo study of a hard-core boson model with ring-only exchanges on a square lattice, where a $K_1$ term acts on $1\times 1$ plaquettes and a $K_2$ term acts on $1\times 2$ and $2\times 1$ plaquettes. At half-filling, the phase diagram reveals charge density wave for small $K_2$, valence bond solid for intermediate $K_2$, and possibly for large $K_2$ the novel exciton Bose liquid (EBL) phase first proposed by Paramekanti et al [Phys. Rev. B 66, 054526 (2002)]. Away from half-filling, the EBL phase is present already for intermediate $K_2$ and remains stable for a range of densities below $1/2$ before phase separation sets in at lower densities.

Figure 1

Structure factors versus $K_2$ for periodic lattices with length $L=6$, 8, 10, and 12, where open symbols are for the density structure factor $S(\pi ,\pi )$, and solid symbols are for the plaquette structure factor $P(\pi ,0)$. Note that linear scale is used for $K_2=0$ to 1 in steps of 0.1, and log scale for $K_2=1$ to 10 in steps of 1.

Figure 2

Top: Finite size scaling of the staggered CDW order parameter $S(\pi ,\pi )/L^2$ at selected $K_2$. Bottom: Finite size scaling of the bond-solid order parameter $P(\pi ,0)/L^2$ at selected $K_2$.

Figure 3

Top: Density structure factor $S(q_x,q_y)$ for a $12\times 12$ lattice at $K_2=5$. Middle: Plaquette structure factor $P(q_x,q_y)$ for the same system. Bottom: Cut of the plaquette structure factor at $q_x=\pi$ for lattice sizes $L=6$, 8, 10, and 12.