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arXiv:2506.16820 · Physical Review Letters

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

Kuangjie Chen, Yang Qi, Zheng Yan, Xiaopeng Li

Published Dec 3, 2025• 0 citations
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Abstract

Recent advances in Rydberg tweezer arrays bring novel opportunities for programmable quantum simulations beyond previous capabilities. In this Letter, 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.

DOI
10.1103/fg7f-zvtt

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Recent advances in Rydberg tweezer arrays bring novel opportunities for programmable quantum simulations beyond previous capabilities. In this Letter, 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.
Rydberg tweezer arrays provide a versatile platform to explore quantum magnets with dipolar XY or van der Waals Ising ZZ interactions. Here, we propose a scheme combining dipolar and van der Waals interactions between two Rydberg states, where the amplitude of the latter can be greater than that of the former, realizing an extended Hubbard model with long-range tunnelings in optical tweezer arrays. On the triangular lattice with repulsive interactions, we predict the existence of a robust supersolid phase with a critical entropy per particle S / N ≈ 0.19 accessible in current Rydberg tweezer experiments supported by large-scale quantum Monte Carlo simulations. We further demonstrate the experimental feasibility by identifying pairs of Rydberg states in Rb 87 realizing the required interactions. Such a lattice supersolid is long lived, found over a wide parameter range in an isotropic and flat two-dimensional geometry, and can be realized for hundreds of particles allowing one to directly probe the defect-induced picture of supersolids. Its thermodynamical and dynamical properties can hence be studied at a far larger scale than hitherto possible.
Recent experiments with ultracold Rydberg-excited atoms have shown that long-range interactions can give rise to spatially ordered structures. Observation of crystalline phases in a system with Rydberg atoms loaded into an optical lattice seems also within reach. Here we investigate a bosonic model on a triangular lattice suitable for description of such experiments. Numerical simulations based on bosonic dynamical mean-field theory reveal a rich phase diagram with different supersolid phases. Comparison with the results obtained for a square lattice geometry shows qualitatively similar results in a wide range of parameters; however, on a triangular lattice we do not observe the checkerboard supersolid. Moreover, unlike on a square lattice, we did not find a phase transition from uniform superfluid to supersolid induced by increase of the hopping amplitude on a triangular lattice. Based on our results, we propose an intuitive interpretation of the nature of different supersolid phases. We also propose parameters for the experimental realization.
Rydberg and Rydberg-dressed atomic gases have recently emerged as a promising quantum simulator for a variety of models in condensed matter physics. Here we investigate one-dimensional bosons with soft-core Rydberg-dressed interactions using exact path-integral quantum Monte Carlo simulations. The finite-range and the negative Fourier component of the interaction potential generate a roton mode at finite momentum, while particle-hole backscattering processes enhance the susceptibility of one-dimensional systems at twice the Fermi momentum. The competition between the corresponding length scales yields a rich phase diagram, featuring a conventional Tomonaga-Luttinger liquid (TLL) regime, a beyond-TLL regime, and commensurate cluster phases. In the TLL regime, the system transitions from Lieb-Liniger-like bnehavior with Luttinger parameter K>1K>1K>1 to hard-rod-like behavior with K<1K<1K<1, with a quasi-supersolid phase emerging for K<1/2K < 1/2K<1/2. For strong interactions and high densities, deviations from TLL theory appear as precursors for the onset of cluster phases, where particles aggregate into stable clusters of several particles. The properties of each phase is discussed in detail.
Inspired by the recent experimental advances in cold atom quantum simulators, we explore the experimentally implemented bosonic t-t^{'}-J model on the square lattice using large-scale density matrix renormalization group simulations. By tuning the doping level δ and hopping ratio t^{'}/t, we uncover six distinct quantum phases, several of which go far beyond the conventional paradigm of phase-coherent superfluidity (SF) expected for bosonic systems. In particular, in the presence of antiferromagnetic (AFM) order, doped holes are tightly bound into pairs, giving rise to a pair density wave phase at low doping and small |t^{'}/t|, which is suppressed on the t^{'}<0 side, resulting in a disordered pair density wave state that lacks coherence of either individual bosons or pairs. Upon further doping, bosons can regain phase coherence and form an SF* state, characterized by condensation at emergent incommensurate momenta concurrent with an incommensurate magnetic order. On the t^{'}>0 side, the sign-induced kinetic frustration inherently disfavors local AFM correlations, leading to a phase separation in which doped holes cluster into ferromagnetic (FM) domains spatially separated by undoped AFM regions. Upon further doping, this inhomogeneous state evolves into a uniform SF+xy-FM phase. Finally, we propose a concrete experimental scheme to realize both signs of t^{'}/t in Rydberg tweezer arrays, with an explicit mapping between model parameters and experimentally accessible regimes. Our results reveal competing and intertwined orders in doped antiferromagnets, which are relevant to central issues in high-T_{c} superconductivity, reflecting the frustrated interplay between doped holes and spin background.
We have studied by quantum Monte Carlo simulations the low temperature phase diagram of a mixture of isotopic, hard core bosons, described by the $t\text{\ensuremath{-}}{J}_{z}\text{\ensuremath{-}}{J}_{\ensuremath{\perp}}$ model, with ${J}_{\ensuremath{\perp}}=\ensuremath{\alpha}{J}_{z}$. The coexistence of superfluid hole-rich and insulating, antiferromagnetically ordered hole-free phases is observed at sufficiently low hole density for any $\ensuremath{\alpha}<1$. A two-component checkerboard supersolid phase is not observed. The experimental relevance and possible broader implications of these findings are discussed.
A programmable quantum simulator using Rydberg-atom array provides a promising route to demystifying quantum many-body physics in strongly correlated systems. Motivated by the recent realization of various quantum magnetic phases on the frustrated Rydberg-atom array, we perform numerically exact quantum Monte Carlo simulations to investigate the exotic states of matter emerging in the model describing the Rydberg atom on a triangular lattice. Our state-of-the-art simulation unveils the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ triangular antiferromagnetic order exists at 1/31/31/3 or 2/32/32/3-Rydberg filling, consistent with the observation in experiments. Remarkably, $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ long-range order arising from order-by-disorder mechanism emerges at 1/21/21/2 filling. At finite temperature, U(1)\mathrm{U}(1)U(1) symmetry is emergent at 1/21/21/2 filling and a Kosterlitz-Thouless phase transition occurs with increasing temperature. These intriguing phenomena are potentially detected in future Rydberg-atom experiments.