[Paper Review] Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array

M. W. Kalinowski, Rhine Samajdar+4 more|arXiv (Cornell University)|Dec 20, 2021

Cold Atom Physics and Bose-Einstein Condensates82 references44 citations

TL;DR

This paper investigates quantum phase transitions in a square Rydberg atom array using large-scale quantum Monte Carlo simulations and Landau-Ginzburg-Wilson field theory. It identifies first-order transitions between disordered, checkerboard, striated, and star phases under periodic boundary conditions, while revealing a novel second-order boundary quantum phase transition under open boundaries—explaining experimental adiabatic state preparation success despite first-order bulk transitions.

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.

Motivation & Objective

• To classify quantum phase transitions in a 2D square Rydberg atom array with realistic long-range interactions.
• To determine whether transitions between ordered phases (checkerboard, striated, star) are continuous or first-order.
• To explain the discrepancy between theoretical first-order transitions and successful experimental adiabatic preparation of ordered states.
• To investigate the role of boundary conditions in inducing independent quantum phase transitions.
• To develop a unified field-theoretic description using Landau-Ginzburg-Wilson theory for the observed transitions.

Proposed method

• Performs large-scale quantum Monte Carlo simulations on systems with periodic boundary conditions to map the phase diagram.
• Uses finite-size scaling of order parameters and Binder ratios to distinguish second-order from first-order transitions.
• Constructs low-energy Landau-Ginzburg-Wilson field theories to analytically describe the nature of quantum critical points.
• Identifies fluctuation-induced first-order transitions via renormalization group flow analysis.
• Analyzes systems with open boundary conditions to detect boundary-ordered phases independent of bulk order.
• Employs momentum-space Fourier transforms of Rydberg density to define order parameters for checkerboard, striated, and star phases.

Experimental results

Research questions

• RQ1 Are the quantum phase transitions between the disordered, checkerboard, striated, and star phases continuous or first-order in a square Rydberg atom array?
• RQ2 Why do experiments successfully prepare ordered phases via adiabatic evolution despite theoretical predictions of first-order transitions?
• RQ3 Can boundary conditions induce a quantum phase transition independent of the bulk in Rydberg systems?
• RQ4 What is the origin of first-order transitions in this system, and how do fluctuations affect the renormalization group flow?
• RQ5 How does the presence of a boundary alter the phase diagram, particularly the extent of the striated phase?

Key findings

• The transition from the disordered phase to the checkerboard phase is continuous, while the transition to the striated and star phases is first-order.
• The transition from the checkerboard to the striated phase is continuous, confirmed by finite-size scaling of the Binder ratio.
• First-order transitions arise from fluctuation-induced instabilities, with no stable fixed points in the renormalization group flow.
• Under open boundary conditions, the system exhibits a second-order quantum phase transition at the boundary, independent of the bulk.
• The boundary transition reduces the effective first-order character of bulk transitions, enabling experimental adiabatic state preparation in intermediate-sized systems.
• The phase diagram is significantly modified by boundaries, with the striated phase extending further under open conditions.