Quantum Domain Walls Induce Incommensurate Supersolid Phase on the Anisotropic Triangular Lattice

We investigate the extended hard-core Bose-Hubbard model on the triangular lattice as a function of spatial anisotropy with respect to both hopping and nearest-neighbor interaction strength. At half-filling the system can be tuned from decoupled one-dimensional chains to a two-dimensional solid phase with alternating density order by adjusting the anisotropic coupling. At intermediate anisotropy, however, frustration effects dominate and an incommensurate supersolid phase emerges, which is characterized by incommensurate density order as well as an anisotropic superfluid density. We demonstrate that this intermediate phase results from the proliferation of topological defects in the form of quantum bosonic domain walls. Accordingly, the structure factor has peaks at wave vectors, which are linearly related to the number of domain walls in a finite system in agreement with extensive quantum Monte Carlo simulations. We discuss possible connections with the supersolid behavior in the high-temperature superconducting striped phase.

Figure 1

(a) Configuration of the checkered solid phase when $V^{\prime }\gg V$ (inset: notation for hoppings and interactions); (b) Single bosonic domain wall (red line) is excited for larger $\eta$. Kinks can fluctuate by particle hopping to new shape (green); (c) multidomain wall case; (d) decoupled chain phase when $V^{\prime }\ll V$, thick lines indicate strong interactions and order in the $x$ direction; (e) structure factors of phases with different numbers of domain walls (from left to right: $N_D=0$, 2, 4, 6, 8, 10, and 12) for lattice size $L_x=L_y=12$ and pbc. The first Brillouin zone is indicated by shading and the red box marks the commensurate supersolid ($\eta =1$).

Figure 2

Bosonic domain wall density (4) as a function of anisotropy parameter $\eta$ for $L=24$ with pbc at $t^{\prime }/V^{\prime }=0.08$ and $\beta V_{\max }=400$ from QMC (dots) compared to the analytical predictions from Eqs. (5) (red) and (6) (black), respectively. Inset: Finite-size scaling of the left and right points of the commensurate supersolid plateau (${\rho }_D=2/3$) with a second-order polynomial fit.

Figure 3

Total superfluid density ${\rho }_s={\rho }_s^x+{\rho }_s^y$, its value in the $y$ direction ${\rho }_s^y$, and structure factor $S(\mathbf{Q})/N$ at $t/V=0.08$, $\beta V_{\max }=400$, and $L=24$.