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

Fuente: arXiv
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Main Authors: Maruyama, Isao, Miyahara, Shin
Format: Preprint
Published: 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
id 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