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arXiv · 2609.31319

Criticality enabled long-range order in a U(1)-symmetric spin-1 Heisenberg chain with biquadratic interactions

Natalia Chepiga·Fabian H. L. Essler
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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 $(S^x,S^y)$ 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 $β\approx0.29$, consistent with the $ε$-expansion prediction $β\approx0.28$, 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 $z\approx2$. Our results support the critical behavior predicted by Nahum's field theory.

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Natalia Chepiga, Fabian H. L. Essler. 2026-09-25. Criticality enabled long-range order in a U(1)-symmetric spin-1 Heisenberg chain with biquadratic interactions. https://arxiv.org/abs/2609.31319

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