Generalization of the Affleck-Kennedy-Lieb-Tasaki Model for Quantum Ferromagnetism
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arXiv
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| Format: | Preprint |
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2025
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| author | Maruyama, Isao Miyahara, Shin |
| author_facet | Maruyama, Isao Miyahara, Shin |
| contents | We study a spin-$S$ ferromagnetic model with exactly-written ground states, known as the partially-magnetized valence bond solid (VBS) states with magnetization $m=(S-1)/S$, which is a ferromagnetic generalization of the Affleck-Kennedy-Lieb-Tasaki model. We find that the VBS state and an antiferromagnetic ground state with magnetization $m=0$ are degenerate for $S=3/2$ and $S=2$ by using the Lanczos method and the density matrix renormalization group method (DMRG). However, increasing $S$, the magnetization of the ground states is uniquely determined as the fraction $m=(S-1)/S$. This is not just a ferromagnet, but a quantum ferromagnet due to quantum entanglement inherent in VBS states. In the low-energy excitation spectrum, we find the coexistence of the Haldane gap and Goldstone-like ferromagnetic magnon excitation. This ``magnetic chimera'' clearly appears under a finite magnetic field. Finally, we discuss an application to the measurement-based quantum computation and an extension of the Haldane's conjecture. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_11537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalization of the Affleck-Kennedy-Lieb-Tasaki Model for Quantum Ferromagnetism Maruyama, Isao Miyahara, Shin Strongly Correlated Electrons Statistical Mechanics We study a spin-$S$ ferromagnetic model with exactly-written ground states, known as the partially-magnetized valence bond solid (VBS) states with magnetization $m=(S-1)/S$, which is a ferromagnetic generalization of the Affleck-Kennedy-Lieb-Tasaki model. We find that the VBS state and an antiferromagnetic ground state with magnetization $m=0$ are degenerate for $S=3/2$ and $S=2$ by using the Lanczos method and the density matrix renormalization group method (DMRG). However, increasing $S$, the magnetization of the ground states is uniquely determined as the fraction $m=(S-1)/S$. This is not just a ferromagnet, but a quantum ferromagnet due to quantum entanglement inherent in VBS states. In the low-energy excitation spectrum, we find the coexistence of the Haldane gap and Goldstone-like ferromagnetic magnon excitation. This ``magnetic chimera'' clearly appears under a finite magnetic field. Finally, we discuss an application to the measurement-based quantum computation and an extension of the Haldane's conjecture. |
| title | Generalization of the Affleck-Kennedy-Lieb-Tasaki Model for Quantum Ferromagnetism |
| topic | Strongly Correlated Electrons Statistical Mechanics |
| url | https://arxiv.org/abs/2509.11537 |