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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.00211 |
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| _version_ | 1866911734846980096 |
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| author | O'Brien, Matthew C. Fradkin, Eduardo |
| author_facet | O'Brien, Matthew C. Fradkin, Eduardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00211 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vestigial Nematic Order at Zero Temperature in Two-Dimensional Frustrated Quantum Antiferromagnets O'Brien, Matthew C. Fradkin, Eduardo Strongly Correlated Electrons 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. |
| title | Vestigial Nematic Order at Zero Temperature in Two-Dimensional Frustrated Quantum Antiferromagnets |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2606.00211 |