The one-dimensional lattice Schwinger model has recently been realized by using bosons in optical lattices.This model contains both confinement and deconfinement phases, the phase diagram of which is controlled by the mass of the matter field and the topological angle.Since varying the mass of the matter field is straightforward experimentally, we propose how to tune the topological angle, allowing exploration of the phase diagram from both directions.We propose that direct experimental evidence of confinement and deconfinement can be obtained by measuring whether a physical charge is localized around a fixed gauge charge to screen it.We also discuss the PXP model realized in the Rydberg-atom array, which is equivalent to the lattice Schwinger model when all local gauge charges are fixed as zero.Although the gauge charges are fixed, we can alternatively probe confinement and deconfinement in the PXP model by studying the relative motion of a pair of a physical charge and an anticharge.Our scheme can be directly implemented in these two relevant experimental platforms of ultracold-atom quantum simulators.
The physical realization of Z 2 topological order as encountered in the paradigmatic toric code has proven to be an elusive goal.We predict that this phase of matter can be realized in a two-dimensional array of Rydberg atoms placed on the ruby lattice, at specific values of the Rydberg blockade radius.First, we show that the blockade model-also known as a "PXP" model-realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term.This model can be interpreted as a Z 2 gauge theory whose dynamics is generated by monomer fluctuations.We obtain its phase diagram using the numerical density matrix renormalization group method and find a topological quantum liquid (TQL) as evidenced by multiple measures including (i) a continuous transition between two featureless phases, (ii) a topological entanglement entropy of ln 2 as measured in various geometries, (iii) degenerate topological ground states, and (iv) the expected modular matrix from ground state overlap.Next, we show that the TQL persists upon including realistic, algebraically decaying van der Waals interactions VðrÞ ∼ 1=r 6 for a choice of lattice parameters.Moreover, we can directly access topological loop operators, including the Fredenhagen-Marcu order parameter.We show how these can be measured experimentally using a dynamic protocol, providing a "smoking gun" experimental signature of the TQL phase.Finally, we show how to trap an emergent anyon and realize different topological boundary conditions, and we discuss the implications for exploring fault-tolerant quantum memories.
The Rydberg blockade induces strongly correlated many-body effects in Rydberg atom arrays, including rich ground-state phases and many-body scar states in the excitation spectrum.In this Letter, we propose a composite spin representation that can provide a unified description for major features in this system.The composite spin combines Rydberg excitation and the auxiliary fermions, which are introduced to implement the Rydberg blockade constraint automatically.First, we focus on the PXP model describing one-dimensional arrays with the Rydberg blocking radius being a lattice spacing.Using composite spins, the ground state is simply a polarized product state of composite spins, and the magnon excitations of these composite spins can accurately describe the many-body scar states and signal the quantum phase transition driven by detuning.Then, we show that Rydberg atom arrays with different blocking radii can share a universal description in terms of the composite spin representation, and the difference between different blockade radii can be absorbed in the formation of composite spins.Hence, our scheme provides a universal physical picture of the blockade effect in Rydberg atom arrays.
Arrays of Rydberg atoms have appeared as a remarkably rich playground to study quantum phase transitions in one dimension. One of the biggest puzzles that was brought forward in this context are chiral phase transitions out of density waves. Theoretically predicted chiral transition out of period-four phase is still pending experimental verification mainly due to extremely short interval over which this transition is realized in a single-component Rydberg array. In this Letter, we show that multicomponent Rydberg arrays with extra experimentally tunable parameters provide a mechanism to manipulate quantum critical properties without breaking translation symmetry explicitly. We consider an effective blockade model of two component Rydberg atoms. Weak and strong components obey nearest- and next-nearest-neighbor blockades correspondingly. When laser detuning is applied to either of the two components the system is in the period-3 and period-2 phases. But laser detuning applied to both components simultaneously stabilizes the period-4 phase partly bounded by the chiral transition. We show that relative ratio of the Rabi frequencies of the two components tunes the properties of the conformal Ashkin-Teller point and allows us to manipulate an extent of the chiral transition. The prospects of multicomponent Rydberg arrays in the context of critical fusion is briefly discussed.
Recent atomic physics experiments and numerical works have reported complementary signatures of the emergence of a topological quantum spin liquid in models with blockade interactions. However, the specific mechanism stabilizing such a phase remains unclear. Here, we introduce an exact relation between an Ising-Higgs lattice gauge theory on the kagome lattice and blockaded models on Ruby lattices. This relation elucidates the origin of previously observed topological spin liquids by directly linking the latter to a deconfined phase of a solvable gauge theory. By means of exact diagonalization and unbiased quantum Monte Carlo simulations, we show that the deconfined phases extend in a broad region of the parameter space; these states are characterized by a large ground state overlap with resonating valence bond wave functions. These blockaded models include both creation or annihilation and hopping dynamics, and can be experimentally realized with Rydberg-dressed atoms, offering novel and controllable platforms for the engineering and characterization of spin liquid states.
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.