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

arXiv:2609.31319 · cond-mat.str-el, quant-ph · Submitted 2026-09-25 · Read on arXiv

cond-mat.str-el, quant-ph

Submitted: 2026-09-25

Updated: 2026-09-25

Comments: 21 pages, 16 figures

License: http://creativecommons.org/licenses/by/4.0/

The gist: 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

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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 about0.29, consistent with the ε-expansion prediction β about0.28, 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 about2. Our results support the critical behavior predicted by Nahum's field theory.

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