Magnetic Phases of Spatially-Modulated Spin-1 Chains in Rydberg Excitons: Classical and Quantum Simulations

TL;DR

This paper explores the magnetic phases of a spatially-modulated spin-1 Rydberg exciton chain, analyzing topological and magnetic properties through classical and quantum simulation methods, including a novel hybrid quantum algorithm.

Contribution

It introduces a hybrid quantum algorithm using Restricted Boltzmann Machines to simulate ground states of spin-1 chains, validated against DMRG and exact diagonalization.

Findings

Identification of various magnetic and topological phases

Robustness analysis of the Haldane phase

Successful implementation of a hybrid quantum simulation method

Abstract

In this work, we study the magnetic phases of a spatially-modulated chain of spin-1 Rydberg excitons. Using the Density Matrix Renormalization Group (DMRG) technique we study various magnetic and topologically nontrivial phases using both single-particle properties like local magnetization and quantum entropy as well as many-body ones like pair-wise N\'eel and long-range string correlations. In particular, we investigate the emergence and robustness of Haldane phase, a topological phase of anti-ferromagnetic spin-1 chains. Further, we devise a hybrid quantum algorithm employing Restricted Boltzmann Machine to simulate the ground state of such a system which shows very good agreement with the results of exact diagonalization (ED) and DMRG.