Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice

TL;DR

This study employs two-dimensional recurrent neural network wave functions to investigate the ground states of Rydberg atom arrays on the kagome lattice, finding no evidence of exotic phases and highlighting the benefits of RNNs in quantum simulations.

Contribution

The paper introduces the use of 2D RNN wave functions with annealing to explore frustrated Rydberg atom systems, demonstrating their effectiveness in studying complex quantum phases.

Findings

RNN ground states show no evidence of spin liquids or glassy behavior.

Autocorrelation issues in QMC can be mitigated by increasing computational effort.

RNNs are useful for exploring frustrated quantum systems.

Abstract

Rydberg atom array experiments have demonstrated the ability to act as powerful quantum simulators, preparing strongly-correlated phases of matter which are challenging to study for conventional computer simulations. A key direction has been the implementation of interactions on frustrated geometries, in an effort to prepare exotic many-body states such as spin liquids and glasses. In this paper, we apply two-dimensional recurrent neural network (RNN) wave functions to study the ground states of Rydberg atom arrays on the kagome lattice. We implement an annealing scheme to find the RNN variational parameters in regions of the phase diagram where exotic phases may occur, corresponding to rough optimization landscapes. For Rydberg atom array Hamiltonians studied previously on the kagome lattice, our RNN ground states show no evidence of exotic spin liquid or emergent glassy behavior. In the latter case, we argue that the presence of a non-zero Edwards-Anderson order parameter is an artifact of the long autocorrelations times experienced with quantum Monte Carlo (QMC) simulations, and we show that autocorrelations can be systematically reduced by increasing numerical effort. This result emphasizes the utility of autoregressive models, such as RNNs, in conjunction with QMC, to explore Rydberg atom array physics on frustrated lattices and beyond.