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.

中文翻译：

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里德堡激子中空间调制自旋 1 链的磁相：经典和量子模拟

在这项工作中，我们研究了空间调制的自旋 1 里德堡激子链的磁相。使用密度矩阵重整化群 (DMRG) 技术，我们使用局部磁化和量子熵等单粒子特性以及成对 N\'eel 和长程弦等多体特性来研究各种磁性和拓扑非平凡相相关性。特别是，我们研究了 Haldane 相的出现和稳健性，这是一种反铁磁自旋 1 链的拓扑相。此外，我们设计了一种混合量子算法，使用受限玻尔兹曼机来模拟这种系统的基态，该算法与精确对角化 (ED) 和 DMRG 的结果非常吻合。