Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies

IF 6.6 1区 物理与天体物理 Q1 PHYSICS, APPLIED npj Quantum Information Pub Date : 2024-11-06 DOI:10.1038/s41534-024-00900-2
Roeland Wiersema, Efekan Kökcü, Alexander F. Kemper, Bojko N. Bakalov
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Abstract

Much is understood about 1-dimensional spin chains in terms of entanglement properties, physical phases, and integrability. However, the Lie algebraic properties of the Hamiltonians describing these systems remain largely unexplored. In this work, we provide a classification of all Lie algebras generated by the terms of 2-local spin chain Hamiltonians, or so-called dynamical Lie algebras, on 1-dimensional linear and circular lattice structures. We find 17 unique dynamical Lie algebras. Our classification includes some well-known models such as the transverse-field Ising model and the Heisenberg chain, and we also find more exotic classes of Hamiltonians that appear new. In addition to the closed and open spin chains, we consider systems with a fully connected topology, which may be relevant for quantum machine learning approaches. We discuss the practical implications of our work in the context of variational quantum computing, quantum control and the spin chain literature.

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线性拓扑、环状拓扑和全连接拓扑上的 2 局域自旋系统动态列阵的分类
人们对一维自旋链的纠缠特性、物理相位和可积分性有了很多了解。然而,描述这些系统的哈密顿的列代数性质在很大程度上仍未得到探索。在这项研究中,我们对一维线性和环形晶格结构上由 2 局域自旋链哈密顿项生成的所有列代数,即所谓的动力学列代数进行了分类。我们发现了 17 个独特的动态李代数。我们的分类包括一些众所周知的模型,如横向场伊辛模型和海森堡链,同时我们还发现了更多新颖奇特的哈密顿。除了封闭和开放的自旋链,我们还考虑了具有全连接拓扑的系统,这可能与量子机器学习方法有关。我们将结合变分量子计算、量子控制和自旋链文献,讨论我们工作的实际意义。
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来源期刊
npj Quantum Information
npj Quantum Information Computer Science-Computer Science (miscellaneous)
CiteScore
13.70
自引率
3.90%
发文量
130
审稿时长
29 weeks
期刊介绍: The scope of npj Quantum Information spans across all relevant disciplines, fields, approaches and levels and so considers outstanding work ranging from fundamental research to applications and technologies.
期刊最新文献
Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies Time-optimal control of a solid-state spin amidst dynamical quantum wind Qubit teleportation between a memory-compatible photonic time-bin qubit and a solid-state quantum network node An architecture for two-qubit encoding in neutral ytterbium-171 atoms
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