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Vestigial Nematic Order at Zero Temperature in Two-Dimensional Frustrated Quantum Antiferromagnets

  • Matthew C. O'Brien
  • Eduardo Fradkin
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Abstract

The phase diagram of the two-dimensional quantum J1-J3 Heisenberg antiferromagnet on a square lattice is a long-standing open problem. Despite recent advances in numerical techniques for quantum spin models, a detailed analytical theory is still lacking. We address this problem using a semiclassical approach based on a continuum nonlinear sigma model effective field theory, applying the nonperturbative large-N technique to map out the phase diagram and determine the magnetic correlations. We show that previously-overlooked interactions are crucial for stabilizing a vestigial nematic phase, both at finite and zero temperature. Our results reveal that the spontaneous breaking of global symmetries in the J1-J3 model is controlled by the strength of infrared quantum fluctuations which are enhanced by proximity to the classical Lifshitz point.

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Cite

BibTeXRIS
BibTeX
@misc{obrien2026vestigial,
  title = {{Vestigial Nematic Order at Zero Temperature in Two-Dimensional Frustrated Quantum Antiferromagnets}},
  author = {Matthew C. O'Brien and Eduardo Fradkin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.00211},
  eprint = {2606.00211},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.00211},
}
RIS
TY  - UNPB
TI  - Vestigial Nematic Order at Zero Temperature in Two-Dimensional Frustrated Quantum Antiferromagnets
AU  - Matthew C. O'Brien
AU  - Eduardo Fradkin
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2606.00211
UR  - https://arxiv.org/abs/2606.00211
AB  - The phase diagram of the two-dimensional quantum J_1-J_3 Heisenberg antiferromagnet on a square lattice is a long-standing open problem. Despite recent advances in numerical techniques for quantum spin models, a detailed analytical theory is still lacking. We address this problem using a semiclassical approach based on a continuum nonlinear sigma model effective field theory, applying the nonperturbative large-N technique to map out the phase diagram and determine the magnetic correlations. We show that previously-overlooked interactions are crucial for stabilizing a vestigial nematic phase, both at finite and zero temperature. Our results reveal that the spontaneous breaking of global symmetries in the J_1-J_3 model is controlled by the strength of infrared quantum fluctuations which are enhanced by proximity to the classical Lifshitz point.
ER  -