Periodic Motzkin chain: Ground states and symmetries
Motzkin chain is a model of nearest-neighbor interacting quantum s=1 spins with open boundary conditions. It is known that it has a unique ground state which can be viewed as a sum of Motzkin paths. We consider the case of periodic boundary conditions and provide several conjectures about structure...
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| Format: | Article |
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Elsevier
2025-08-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321325001725 |
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| _version_ | 1849731864063901696 |
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| author | Andrei G. Pronko |
| author_facet | Andrei G. Pronko |
| author_sort | Andrei G. Pronko |
| collection | DOAJ |
| description | Motzkin chain is a model of nearest-neighbor interacting quantum s=1 spins with open boundary conditions. It is known that it has a unique ground state which can be viewed as a sum of Motzkin paths. We consider the case of periodic boundary conditions and provide several conjectures about structure of the ground state space and symmetries of the Hamiltonian. We conjecture that the ground state is degenerate and independent states are distinguished by eigenvalues of the third component of total spin operator. Each of these states can be described as a sum of paths, similar to the Motzkin paths. Moreover, there exist two operators commuting with the Hamiltonian, which play the roles of lowering and raising operators when acting at these states. We conjecture also that these operators generate a C-type Lie algebra, with rank equal to the number of sites. The symmetry algebra of the Hamiltonian is actually wider, and extended, besides the cyclic shift operator, by a central element contained in the third component of total spin operator. |
| format | Article |
| id | doaj-art-7384b43394114e4485804f16cf0d8d97 |
| institution | DOAJ |
| issn | 0550-3213 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj-art-7384b43394114e4485804f16cf0d8d972025-08-20T03:08:24ZengElsevierNuclear Physics B0550-32132025-08-01101711696310.1016/j.nuclphysb.2025.116963Periodic Motzkin chain: Ground states and symmetriesAndrei G. Pronko0Steklov Mathematical Institute, Fontanka 27, 191023 Saint Petersburg, RussiaMotzkin chain is a model of nearest-neighbor interacting quantum s=1 spins with open boundary conditions. It is known that it has a unique ground state which can be viewed as a sum of Motzkin paths. We consider the case of periodic boundary conditions and provide several conjectures about structure of the ground state space and symmetries of the Hamiltonian. We conjecture that the ground state is degenerate and independent states are distinguished by eigenvalues of the third component of total spin operator. Each of these states can be described as a sum of paths, similar to the Motzkin paths. Moreover, there exist two operators commuting with the Hamiltonian, which play the roles of lowering and raising operators when acting at these states. We conjecture also that these operators generate a C-type Lie algebra, with rank equal to the number of sites. The symmetry algebra of the Hamiltonian is actually wider, and extended, besides the cyclic shift operator, by a central element contained in the third component of total spin operator.http://www.sciencedirect.com/science/article/pii/S0550321325001725 |
| spellingShingle | Andrei G. Pronko Periodic Motzkin chain: Ground states and symmetries Nuclear Physics B |
| title | Periodic Motzkin chain: Ground states and symmetries |
| title_full | Periodic Motzkin chain: Ground states and symmetries |
| title_fullStr | Periodic Motzkin chain: Ground states and symmetries |
| title_full_unstemmed | Periodic Motzkin chain: Ground states and symmetries |
| title_short | Periodic Motzkin chain: Ground states and symmetries |
| title_sort | periodic motzkin chain ground states and symmetries |
| url | http://www.sciencedirect.com/science/article/pii/S0550321325001725 |
| work_keys_str_mv | AT andreigpronko periodicmotzkinchaingroundstatesandsymmetries |