Criticality enabled long-range order in a U(1)-symmetric spin-1 Heisenberg chain with biquadratic interactions
Abstract
In a recent paper Nahum argued on the basis of a renormalization-group analysis that, contrary to standard lore, ground states of 1D spin chains with short-range interactions can spontaneously break U(1) ``easy-plane'' spin rotation symmetry. True long-range order of (Sx,Sy) arises at the phase transition between two quasi-long-range-ordered phases. Here we present detailed numerical results for an anisotropic spin-1 chain model. We find a magnetization exponent β≈0.29, consistent with the ε-expansion prediction β≈0.28, a divergence of the Luttinger parameter on approaching the transition from both sides with an exponent that we relate to Nahum's transition, and finite-size spectra consistent with a dynamical critical exponent z≈2. Our results support the critical behavior predicted by Nahum's field theory.
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BibTeX
@misc{chepiga2026criticality,
title = {{Criticality enabled long-range order in a U(1)-symmetric spin-1 Heisenberg chain with biquadratic interactions}},
author = {Natalia Chepiga and Fabian H. L. Essler},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31319},
eprint = {2609.31319},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31319},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Criticality enabled long-range order in a U(1)-symmetric spin-1 Heisenberg chain with biquadratic interactions
AU - Natalia Chepiga
AU - Fabian H. L. Essler
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31319
UR - https://arxiv.org/abs/2609.31319
AB - In a recent paper Nahum argued on the basis of a renormalization-group analysis that, contrary to standard lore, ground states of 1D spin chains with short-range interactions can spontaneously break U(1) ``easy-plane'' spin rotation symmetry. True long-range order of (S^x,S^y) arises at the phase transition between two quasi-long-range-ordered phases. Here we present detailed numerical results for an anisotropic spin-1 chain model. We find a magnetization exponent β≈0.29, consistent with the ε-expansion prediction β≈0.28, a divergence of the Luttinger parameter on approaching the transition from both sides with an exponent that we relate to Nahum's transition, and finite-size spectra consistent with a dynamical critical exponent z≈2. Our results support the critical behavior predicted by Nahum's field theory.
ER -