Onset of a quantum Fisher-Selke sequence in the transverse-field ANNNI model and its bilayer
Abstract
We study the transverse-field axial next-nearest-neighbor Ising (ANNNI) model on the square lattice and on a bilayer. At the classical multiphase point κ=J2/J0=1/2, every configuration of straight domain walls that separates domains of at least two sites is a ground state. The walls are rigid, so perturbation theory in the transverse field g=Γ/J0 can be carried out for each configuration separately, and we take it to order g8. Quantum fluctuations select ⟨ 3⟩ (↑↑↑↓↓↓) at order g2, because spins next to a wall gain the most energy from virtual flips. The structures ⟨ 23⟩, ⟨ 223⟩ and ⟨ 2223⟩ then open between ⟨ 3⟩ and the antiphase ⟨ 2⟩ at orders g4, g6 and g8, in the order of the Fisher-Selke sequence of the classical three-dimensional model. A second layer suppresses each successive phase more strongly, beyond the stiffening of the local fields. We test the two widest phases with stochastic series expansion quantum Monte Carlo, comparing the free energies of the competing ordered states by thermodynamic integration, since annealing freezes in the modulation that forms at the ordering transition. The simulations reproduce the ⟨ 3⟩ wedge to about 1%, and in a pre-registered test ⟨ 23⟩ is stable at six of seven points, with the seventh resolved by post-hoc runs.
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BibTeX
@misc{truong2026onset,
title = {{Onset of a quantum Fisher-Selke sequence in the transverse-field ANNNI model and its bilayer}},
author = {Tuan-Vu Truong and Vu-Quoc-Minh Nguyen and Hoang-Long Nguyen and Thanh-Tien Nguyen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05057},
eprint = {2610.05057},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05057},
}
RIS
TY - UNPB
TI - Onset of a quantum Fisher-Selke sequence in the transverse-field ANNNI model and its bilayer
AU - Tuan-Vu Truong
AU - Vu-Quoc-Minh Nguyen
AU - Hoang-Long Nguyen
AU - Thanh-Tien Nguyen
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05057
UR - https://arxiv.org/abs/2610.05057
AB - We study the transverse-field axial next-nearest-neighbor Ising (ANNNI) model on the square lattice and on a bilayer. At the classical multiphase point κ=J_2/J_0=1/2, every configuration of straight domain walls that separates domains of at least two sites is a ground state. The walls are rigid, so perturbation theory in the transverse field g=Γ/J_0 can be carried out for each configuration separately, and we take it to order g^8. Quantum fluctuations select ⟨ 3⟩ (↑↑↑↓↓↓) at order g^2, because spins next to a wall gain the most energy from virtual flips. The structures ⟨ 23⟩, ⟨ 223⟩ and ⟨ 2223⟩ then open between ⟨ 3⟩ and the antiphase ⟨ 2⟩ at orders g^4, g^6 and g^8, in the order of the Fisher-Selke sequence of the classical three-dimensional model. A second layer suppresses each successive phase more strongly, beyond the stiffening of the local fields. We test the two widest phases with stochastic series expansion quantum Monte Carlo, comparing the free energies of the competing ordered states by thermodynamic integration, since annealing freezes in the modulation that forms at the ordering transition. The simulations reproduce the ⟨ 3⟩ wedge to about 1%, and in a pre-registered test ⟨ 23⟩ is stable at six of seven points, with the seventh resolved by post-hoc runs.
ER -