Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array

Abstract

Motivated by recent experimental realizations of exotic phases of matter on programmable quantum simulators, we carry out a comprehensive theoretical study of quantum phase transitions in a Rydberg atom array on a square lattice, with both open and periodic boundary conditions. In the bulk, we identify several first-order and continuous phase transitions by performing large-scale quantum Monte Carlo simulations and develop an analytical understanding of the nature of these transitions using the framework of Landau-Ginzburg-Wilson theory. Remarkably, we find that under open boundary conditions, the boundary itself undergoes a second-order quantum phase transition, independent of the bulk. These results explain recent experimental observations and provide important new insights into both the adiabatic state preparation of novel quantum phases and quantum optimization using Rydberg atom array platforms.

Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays

“…Lastly, we consider the full Rydberg Hamiltonian introduced in Eq. ( 1) of the main text; for this case, we retain the long-ranged tails of the 1/r 6 van der Waals interaction up to a distance of 4a, which was shown to be sufficient for convergence of phase boundaries on the square lattice [85]. Figure S21C shows the minimum quantum gap plotted as a function of the classical hardness parameter HP.…”

Lee-Yang zeros in the Rydberg atoms

“…2. The zeros of the partition function (30) for N = 36. The largest N/3 = 12 of them approach that of r = 2 when V goes to ∞, while the others go to −∞ exponentially, which are omitted in the lower panel.…”

“…Recently, cold Rydberg atoms have attracted extensive research efforts for their versatile control and measurements together with strong dipole interactions. Two major frontiers are unfolding -First, various novel phases and phase transitions emerge from geometries enabled by the single-atom manipulations, including one dimensional (1d) chains [25,26] and two dimensional (2d) square [27][28][29][30] and kagome lattices [31][32][33][34][35]. Even in the seemingly innocuous 1d case, there are some debates on the nature of the phase transitions [36][37][38][39][40][41], a caricature of the rich and subtle physics in such systems.…”

Data-Enhanced Variational Monte Carlo Simulations for Rydberg Atom Arrays

“…State-of-the-art experiments use optical tweezers to arrange and individually address atoms on arbitrary lattices [4][5][6], allowing them to strongly interact with a many-body Hamiltonian [7]. The combination of complex lattice structures together with the precise tuning of inter-atomic interactions has enabled the preparation of various novel phases and phase transitions [6,8,9], whose continuing experimental exploration is supported by a suite of rapidly advancing numerical simulation technologies [10][11][12][13][14].…”

“…In this work, we leverage these unique features of neural network wavefunctions to explore the effect of combined data-and Hamiltonian-driven learning [44]. Beginning with a randomly initialized recurrent neural network (RNN) [18], we first optimize network parameters using a limited amount of simulated [12,14,45] Rydberg occupation data drawn from a two-dimensional array in the vicinity of a quantum phase transition. Then, we continue optimizing the network variationally, in the spirit of the recent work by Carrasquilla and Torlai [33].…”