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arXiv:2509.11537 · Journal of the Physical Society of Japan

Generalization of the Affleck–Kennedy–Lieb–Tasaki Model for Quantum Ferromagnetism

Isao Maruyama, Shin Miyahara

Published Feb 6, 2026• 0 citations
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Abstract

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.

DOI
10.7566/jpsj.95.034704

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We study a spin-SSS ferromagnetic model with exactly-written ground states, known as the partially-magnetized valence bond solid (VBS) states with magnetization m=(S−1)/Sm=(S-1)/Sm=(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=0m=0m=0 are degenerate for S=3/2S=3/2S=3/2 and S=2S=2S=2 by using the Lanczos method and the density matrix renormalization group method (DMRG). However, increasing SSS, the magnetization of the ground states is uniquely determined as the fraction m=(S−1)/Sm=(S-1)/Sm=(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.
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We investigate the entanglement properties of the valence-bond-solid (VBS) state defined on two-dimensional lattices, which is the exact ground state of the Affleck-Kennedy-Lieb-Tasaki model. It is shown that the entanglement entropy obeys an area law and the nonuniversal prefactor of the leading term is strictly less than ln2\mathrm{ln}2ln2. The analysis of entanglement spectra for various lattices reveals that the reduced density matrix associated with the VBS state is closely related to a thermal density matrix of a holographic spin chain, the spectrum of which is reminiscent of that of the spin-1/2 Heisenberg chain. This correspondence is further supported by comparing the entanglement entropy in the holographic spin chain with conformal field theory predictions.