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PreprintCC BY 4.0arXiv

Tensor network study of deconfined quantum criticality in a one-dimensional spin-phonon model

  • Anton Romen
  • Josef Willsher
  • David Hofmeier
  • Johannes Knolle
  • Michael Knap
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Abstract

Deconfined quantum critical points (DQCPs) describe continuous transitions between ordered phases beyond the Landau paradigm. A simple example is the Néel antiferromagnet (AFM) to valence bond solid (VBS) transition in a 1D antiferromagnetic J1−J2 model. In analogy to the spin-Peierls instability of critical spin chains, DQCPs are predicted to be unstable towards lattice distortions below a critical phonon frequency. In this work, we use tensor network simulations to investigate this instability in the antiferromagnetic J1−J2 model coupled to lattice vibrations. We confirm the stability of DQCP for large phonon frequencies and demonstrate that the transition turns strongly first-order below a critical frequency. The instability is caused by a reduction of the Luttinger parameter due to spin-phonon interactions and we identify the effective theory of the behavior as the double sine-Gordon model. The same effective theory is known to describe the classical Ashkin-Teller model, which enables us to show that the critical endpoint is in the four-state Potts universality class. We argue based on non-linear bosonization that the sign of the double-frequency term is fixed, which provides a microscopic justification for the first-order transition. Furthermore, we provide quantitative numerical scaling results for the phonon spectral function, offering an experimental signature to probe DQCP-phonon coupling in low-dimensional materials.

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Cite

BibTeXRIS
BibTeX
@misc{romen2026tensor,
  title = {{Tensor network study of deconfined quantum criticality in a one-dimensional spin-phonon model}},
  author = {Anton Romen and Josef Willsher and David Hofmeier and Johannes Knolle and Michael Knap},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.06605},
  eprint = {2606.06605},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.06605},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Tensor network study of deconfined quantum criticality in a one-dimensional spin-phonon model
AU  - Anton Romen
AU  - Josef Willsher
AU  - David Hofmeier
AU  - Johannes Knolle
AU  - Michael Knap
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2606.06605
UR  - https://arxiv.org/abs/2606.06605
AB  - Deconfined quantum critical points (DQCPs) describe continuous transitions between ordered phases beyond the Landau paradigm. A simple example is the Néel antiferromagnet (AFM) to valence bond solid (VBS) transition in a 1D antiferromagnetic J_1−J_2 model. In analogy to the spin-Peierls instability of critical spin chains, DQCPs are predicted to be unstable towards lattice distortions below a critical phonon frequency. In this work, we use tensor network simulations to investigate this instability in the antiferromagnetic J_1−J_2 model coupled to lattice vibrations. We confirm the stability of DQCP for large phonon frequencies and demonstrate that the transition turns strongly first-order below a critical frequency. The instability is caused by a reduction of the Luttinger parameter due to spin-phonon interactions and we identify the effective theory of the behavior as the double sine-Gordon model. The same effective theory is known to describe the classical Ashkin-Teller model, which enables us to show that the critical endpoint is in the four-state Potts universality class. We argue based on non-linear bosonization that the sign of the double-frequency term is fixed, which provides a microscopic justification for the first-order transition. Furthermore, we provide quantitative numerical scaling results for the phonon spectral function, offering an experimental signature to probe DQCP-phonon coupling in low-dimensional materials.
ER  -