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  • Letter
  • Open Access

Stability of algebraic spin liquids coupled to quantum phonons

Francesco Ferrari1,*, Josef Willsher2,3,4,*,†, Urban F. P. Seifert5,6, Roser Valentí1, and Johannes Knolle2,3,7

  • *These authors contributed equally to this work.
  • †Contact author: willsher@pks.mpg.de
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Phys. Rev. Research 7, L042053 – Published 5 December, 2025

DOI: https://doi.org/10.1103/9wnn-w8bg

Abstract

Algebraic spin liquids are quantum disordered phases of insulating magnets that exhibit fractionalized gapless excitations and power-law correlations. Quantum spin liquids in this category include the experimentally established one-dimensional (1D) Luttinger liquid, as well as the U(1) Dirac spin liquid (DSL) that has been a focus of recent candidate materials searches. Most notably, several exchange-frustrated Heisenberg materials on the triangular lattice have shown evidence of the U(1) DSL. In this work, we measure the algebraic correlations of spin-singlet excitations in the J1−J2 antiferromagnetic Heisenberg model on the triangular lattice, prompting a detailed investigation of this model’s stability under spin-lattice coupling with dynamical quantum phonons using variational Monte Carlo. As seen before in 1D spin chains, we observe a low-temperature transition from a U(1) DSL to valence bond order and predict the parameter regime where the model realizes a stable DSL ground state. To achieve this, we employ a series of finite-size scaling Ansätze inspired by the low-energy DSL’s conformal description in terms of quantum electrodynamics and show that emergent monopole operators drive the instability. We compare the physics of this transition to the 1D Luttinger liquid throughout our analysis. We derive the regime of stability against spin-Peierls ordering and argue that the DSL ground state might still be achievable in candidate materials, despite its tendency to valence bond solid ordering.

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Phys. Rev. Research 7, L042053– Published 5 December, 2025
  • Received 26 November 2024
  • Accepted 16 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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