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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.06182 |
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| _version_ | 1866909453975027712 |
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| author | Bernardini, Alex E. da Rocha, Roldao |
| author_facet | Bernardini, Alex E. da Rocha, Roldao |
| contents | Solutions of generic $SU(2)\otimes SU(2)$ Hamiltonian eigensystems are obtained through systematic manipulations of quartic polynomial equations. An {\em ansatz} for constructing separable and entangled eigenstate basis, depending on the quartic equation coefficients, is proposed. Besides the quantum concurrence for pure entangled states, the associated thermodynamic statistical ensembles, their partition function, quantum purity and quantum concurrence are shown to be straightforwardly obtained. Results are specialized to a $SU(2)\otimes SU(2)$ structure emulated by lattice-layer degrees of freedom of the Bernal stacked graphene, in a context that can be extended to several mesoscopic scale systems for which the onset from $SU(2)\otimes SU(2)$ Hamiltonians has been assumed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06182 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraic solutions for $SU(2)\otimes SU(2)$ Hamiltonian eigensystems: generic statistical ensembles and a mesoscopic system application Bernardini, Alex E. da Rocha, Roldao Quantum Physics High Energy Physics - Theory Mathematical Physics Solutions of generic $SU(2)\otimes SU(2)$ Hamiltonian eigensystems are obtained through systematic manipulations of quartic polynomial equations. An {\em ansatz} for constructing separable and entangled eigenstate basis, depending on the quartic equation coefficients, is proposed. Besides the quantum concurrence for pure entangled states, the associated thermodynamic statistical ensembles, their partition function, quantum purity and quantum concurrence are shown to be straightforwardly obtained. Results are specialized to a $SU(2)\otimes SU(2)$ structure emulated by lattice-layer degrees of freedom of the Bernal stacked graphene, in a context that can be extended to several mesoscopic scale systems for which the onset from $SU(2)\otimes SU(2)$ Hamiltonians has been assumed. |
| title | Algebraic solutions for $SU(2)\otimes SU(2)$ Hamiltonian eigensystems: generic statistical ensembles and a mesoscopic system application |
| topic | Quantum Physics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2501.06182 |