Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies
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 alge...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-11-01
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| Series: | npj Quantum Information |
| Online Access: | https://doi.org/10.1038/s41534-024-00900-2 |
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| author | Roeland Wiersema Efekan Kökcü Alexander F. Kemper Bojko N. Bakalov |
| author_facet | Roeland Wiersema Efekan Kökcü Alexander F. Kemper Bojko N. Bakalov |
| author_sort | Roeland Wiersema |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1d01bd343fb54e118b4477fa1d805f1d |
| institution | Kabale University |
| issn | 2056-6387 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Quantum Information |
| spelling | doaj-art-1d01bd343fb54e118b4477fa1d805f1d2024-11-10T12:36:24ZengNature Portfolionpj Quantum Information2056-63872024-11-0110111510.1038/s41534-024-00900-2Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologiesRoeland Wiersema0Efekan Kökcü1Alexander F. Kemper2Bojko N. Bakalov3Vector Institute, MaRS CentreDepartment of Physics, North Carolina State UniversityDepartment of Physics, North Carolina State UniversityDepartment of Mathematics, North Carolina State UniversityAbstract 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.https://doi.org/10.1038/s41534-024-00900-2 |
| spellingShingle | Roeland Wiersema Efekan Kökcü Alexander F. Kemper Bojko N. Bakalov Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies npj Quantum Information |
| title | Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies |
| title_full | Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies |
| title_fullStr | Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies |
| title_full_unstemmed | Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies |
| title_short | Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies |
| title_sort | classification of dynamical lie algebras of 2 local spin systems on linear circular and fully connected topologies |
| url | https://doi.org/10.1038/s41534-024-00900-2 |
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