In recent years, programmable Rydberg-atom arrays have been widely used to simulate new quantum phases and phase transitions, generating great interest among theorists and experimentalists. Based on the large-scale density matrix renormalization group method, the ground-state phase diagram of one-dimensional Rydberg chains is investigated with fidelity susceptibility as an efficient diagnostic method. We find that the competition between Rydberg blockade and external detuning produces unconventional phases and phase transitions. As the Rydberg blockade radius increases, the phase transition between disordered and density-wave ordered phases changes from the standard Potts universality class to an unconventional chiral one. As the radius increases further (above Potts point but still close to the tip of the lobe), a very narrow intermediate floating-phase region begins to appear. A concise physical picture is also provided to illustrate the numerical results. Compared with previous studies, this work brings more evidence for commensurate-incommensurate quantum phase transitions in programmable quantum simulators from the perspective of quantum information, showing that fidelity susceptibility can be used to study such phase transitions.
Rydberg atom arrays have recently emerged to be a promising platform for the exploration of exotic quantum phases of matter and quantum phenomena. In this work, we map out the ground-state phase diagram of Rydberg atoms on a honeycomb lattice as a function of the Rydberg blockade radius and the laser detuning by performing large-scale finite-size density matrix renormalization group simulations. Apart from a featureless disordered phase, we find five other intricate long-range density-wave-ordered phases within a relatively wide parameter space. The properties of these quantum phases are analyzed by calculating their Rydberg excitation profiles and static structure factors. In addition, a continuous quantum phase transition belonging to the (2+1)-dimensional Ising universality class is explored by a standard finite-size scaling analysis. Our work implies some different physics, such as the possible nontrivial quantum phase transitions and a highly degenerate string ordered phase, that a honeycomb geometry could bring to the Rydberg system and serves as a numerical guide for possible real experiments.
The floating phase, a critical incommensurate phase, has been theoretically predicted as a potential intermediate phase between crystalline ordered and disordered phases. In this study, we investigate the different quantum phases that arise in ladder arrays comprising up to 92 neutral-atom qubits and experimentally observe the emergence of the quantum floating phase. We analyze the site-resolved Rydberg state densities and the distribution of state occurrences. The site-resolved measurement reveals the formation of domain walls within the commensurate ordered phase, which subsequently proliferate and give rise to the floating phase with incommensurate quasi-long-range order. By analyzing the Fourier spectra of the Rydberg density-density correlations, we observe clear signatures of the incommensurate wave order of the floating phase. Furthermore, as the experimental system sizes increase, we show that the wave vectors approach a continuum of values incommensurate with the lattice. Our work motivates future studies to further explore the nature of commensurate-incommensurate phase transitions and their non-equilibrium physics. The critical floating phase can bridge crystalline orders and the disordered phase. Here, the authors experimentally observe the quantum floating phase in neutral atom qubit arrays, revealing domain walls and incommensurate quasi long-range order, and analyse its emergence via Fourier spectroscopy.
Using density matrix renormalization group simulations on open chains, we map out the wave vector in the incommensurate disordered phase of a realistic model of Rydberg chains with
1/r6 interactions, and we locate and characterize the points along the commensurate lines where the transition out of the period 3 and 4 phases is conformal. We confirm that it is three-state Potts for the period-3 phase, and we show that it is Ashkin-Teller with $\ensuremath{\nu}\ensuremath{\simeq}0.80$ for the period-4 phase. We further show that close to these points, the transition is still continuous, but with a completely different scaling of the wave vector, in agreement with a chiral transition. Finally, we propose to use the conformal points as benchmarks for Kibble-Zurek experiments, defining a roadmap towards a conclusive identification of the chiral universality class.
We study the ground-state phase diagram of Rydberg atoms in a triangular-prism optical tweezer array using the density matrix renormalization group. By tuning the detuning-to-Rabi-frequency ratio and the Rydberg blockade radius, the system realizes several density-wave phases with spontaneous breaking of translational and leg-exchange symmetries. Unlike two-leg Rydberg ladders with
Z2 leg-exchange symmetry, the triangular prism has
D3 symmetry, leading to a richer set of ordered phases and transitions. For blockade radius moderately larger than the lattice spacing, a phase with alternating double and single Rydberg occupancy appears at large detuning. It breaks
Z2 translational and
Z3 rotational symmetry while preserving a rung reflection symmetry. Upon decreasing detuning, it melts through two Berezinskii-Kosterlitz-Thouless transitions with an intermediate critical phase described by a
Z6 clock model. At larger blockade radius, a phase with one Rydberg excitation per triangle and broken
D3 symmetry appears through a first-order transition. When double occupation of neighboring triangles is suppressed, rung-trimerized density waves develop as detuning increases from the disordered phase. Their melting follows the same structure as in Rydberg chains and two-leg ladders: the
Z2 case has Ising critical lines, while the
Z3 and
Z4 cases have chiral critical lines, with Potts and Ashkin-Teller points only on the corresponding commensurate lines. Inside the
Z2 rung-trimerized phase, an entanglement-entropy peak signals a crossover regime with enhanced period-2 density modulation before a first-order transition into a
Z2×D3 phase. Floating phases with incommensurate quasi-long-range order appear between trimerized states of different periods.
We study the fidelity susceptibility of a quantum antiferromagnetic Ising chain with a long-range power-law interaction $1/{r}^{\ensuremath{\alpha}}$ using the large-scale density matrix renormalization group method. We find that the critical adiabatic dimension $\ensuremath{\mu}=2$ and the critical exponent of the correlation length $\ensuremath{\nu}=1$ for arbitrary $\ensuremath{\alpha}>0$, indicating all quantum phase transitions are second-order Ising transitions. In addition, we numerically determine the complete phase diagram for $0<\ensuremath{\alpha}\ensuremath{\le}3$ from the data collapse of the fidelity susceptibility and show that the critical point
hc changes monotonously with respect to $\ensuremath{\alpha}$. This work will shed light on the nature of phase transitions in the quantum long-range antiferromagnetic Ising chain from a quantum information perspective.
Dual-species Rydberg atom arrays extend single-species platforms by introducing competing interaction scales and enhanced quantum fluctuations, enabling phenomena beyond homogeneous settings. In this work, we study the ground-state phase diagram of a one-dimensional dual-species Rydberg atom ladder using large-scale density-matrix renormalization group calculations. We identify disordered phases, multiple ordered phases with
Z2,
Z3, and
Z4 symmetry, as well as floating phases characterized by incommensurate wave vectors and algebraically decaying correlations. Importantly, we observe a smooth crossover between distinct
Z2-ordered regimes, reflecting a reorganization of low-energy degrees of freedom rather than a true phase transition, which is absent in single-species Rydberg arrays. We further uncover a multi-critical point at the boundary between the
Z2⊗Z2 and
Z3⊗Z3 ordered phases, where Ising, chiral, and first-order transition lines intersect. Our results demonstrate that dual-species Rydberg atom arrays provide a unique platform for realizing crossover physics and multi-critical behavior inaccessible in single-species architectures.