Double Supersolid Phase in a Bosonic t-J-V Model with Rydberg Atoms

TL;DR

This paper investigates a bosonic $t$-$J$-$V$ model realized with Rydberg atoms in 2D, uncovering a double supersolid phase (DSS) where lattice order coexists with two broken U(1) symmetries. Using large-scale stochastic series expansion QMC with annealing to navigate challenging first-order regions, the authors map a phase diagram featuring AFM, DSF, and DSS phases, and characterize transitions via Binder cumulants, fidelity susceptibility, and finite-size scaling. Notably, the DSS phase exhibits a nontrivial thermal response, including a thermal compensation ordering where crystalline order can be enhanced by increasing temperature. The results illuminate how long-range tunneling and hole-hole repulsion stabilize exotic quantum phases in Rydberg arrays, offering a concrete experimental platform and guiding future explorations of doped quantum magnetism and related phenomena.

Abstract

Recent advances in Rydberg tweezer arrays bring novel opportunities for programmable quantum simulations beyond previous capabilities. In this work, we investigate a bosonic t-J-V model currently realized with Rydberg atoms. Through large-scale quantum Monte Carlo simulations, we uncover an emergent double supersolid (DSS) phase with the coexistence of two superfluids and crystalline order. Tunable long-range tunneling and repulsive hole-hole interactions enable a rich phase diagram featuring a double superfluid phase, a DSS phase, and an antiferromagnetic insulator. Intriguingly, within the DSS regime we observe an unconventional thermal enhancement of crystalline order. Our results establish the bosonic t-J-V model as a promising and experimentally accessible platform for exploring exotic quantum phases in Rydberg atom arrays.

Figures (18)

• Figure 1: (a) Illustration of the bosonic $t$-$J$-$V$ model on the square lattice. The spin-1/2 and hole degrees of freedom are encoded in three distinct Rydberg states, represented by red ($\ket{\uparrow}$), blue ($\ket{\downarrow}$), and white ($\ket{h}$) circles. Effective tunneling $t$, spin-spin interactions $J^{z}$, $J^{\perp}$, and hole-hole interactions $V$ emerge from the interactions among these Rydberg states. (b) Ground-state phase diagram of the $t$-$J$-$V$ model in the $t$-$V$ plane at fixed parameters $J^{z}=4$, $J^{\perp}=-1$, and $\mu=0$. The phase diagram contains an AFM phase (blue region), a double superfluid (DSF) phase (red region), and a double supersolid (DSS) phase (green region). Insets provide schematic illustrations of each phase, with solid lines indicating phase boundaries.
• Figure 2: (a) Ground-state energy per site $E/N$, (b) hole density $\rho$, (c) AFM order parameter $|m_z|$, and (d) superfluid density $\rho_s$ as functions of $t$ for various system sizes ($L=\beta$). The legend is shown only in (a) since all panels use the same symbols. Blue solid (yellow dashed) lines denote forward (backward) annealing. The red circle in panel (a) marks the discontinuity point in the derivative of the minimum energy identified from the hysteresis. ($V=2$).
• Figure 3: (a) Structure factor $S(\pi,\pi)/N$ (blue solid lines) and superfluid density $\rho_s$ (yellow dashed lines) as functions of $t$ for various system sizes ($L=\beta$). (b) Fidelity susceptibility per site $\chi_{F}/N$ , illustrating the AFM-to-DSS and DSS-to-DSF transitions. ($V=8$).
• Figure 4: Diagonal spin correlations $|C^{z}(\boldsymbol{r})|$ and off-diagonal correlations $C^{xy}(\boldsymbol{r})$, evaluated along the lattice axial direction $\boldsymbol{r}=(r,0)$ and the diagonal direction $\boldsymbol{r}=(r,r)$, are shown in the DSS region (panels (a) and (b), $t=1.25$) and the DSF region (panels (c) and (d), $t=1.6$) for various system sizes ($L=\beta$). ($V=8$).
• Figure 5: (a) Structure factor $S(\pi,\pi)/N$ (blue solid lines) and superfluid density $\rho_s$ (yellow dashed lines) versus temperature $T=1/\beta$ for various system sizes. (b) Hole density $\rho$ versus temperature $T$ is shown for the same four system sizes. ($V=8$ and $t=1.2$).