Transition between critical antiferromagnetic phases in the $J_1$-$J_2$ spin chain
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| Formato: | Preprint |
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2024
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| _version_ | 1866911235495165952 |
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| author | McRoberts, Adam J. Hooley, Chris Green, A. G. |
| author_facet | McRoberts, Adam J. Hooley, Chris Green, A. G. |
| contents | The $J_1$-$J_2$ spin chain is one of the canonical models of quantum magnetism, and has long been known to host a critical antiferromagnetic phase with power-law decay of spin correlations. We show in this Letter that there are, in fact, \textit{two} distinct critical antiferromagnetic phases, where the roles of the local dimer field and its dual field are interchanged: the `Affleck-Haldane' phase near the Heisenberg point $J_2 = 0$, where the dimer field that parametrises local singlet order is gapless and part of a joint $O(4)$ Néel-singlet order parameter; and the `Zirnbauer' phase which appears at sufficiently large ferromagnetic $J_2$, where the dimer field is gapped out and its \textit{dual} field -- the instanton density of the $O(3)$ Néel field -- is critical instead. The phases are so-named because each realises one of the competing pictures for how the $O(3)$ non-linear sigma model with a topological theta term renormalises to the $\mathfrak{\hat{su}}(2)_1$ Wess-Zumino-Witten model. We support these predictions with density matrix renormalisation group calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08095 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transition between critical antiferromagnetic phases in the $J_1$-$J_2$ spin chain McRoberts, Adam J. Hooley, Chris Green, A. G. Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory The $J_1$-$J_2$ spin chain is one of the canonical models of quantum magnetism, and has long been known to host a critical antiferromagnetic phase with power-law decay of spin correlations. We show in this Letter that there are, in fact, \textit{two} distinct critical antiferromagnetic phases, where the roles of the local dimer field and its dual field are interchanged: the `Affleck-Haldane' phase near the Heisenberg point $J_2 = 0$, where the dimer field that parametrises local singlet order is gapless and part of a joint $O(4)$ Néel-singlet order parameter; and the `Zirnbauer' phase which appears at sufficiently large ferromagnetic $J_2$, where the dimer field is gapped out and its \textit{dual} field -- the instanton density of the $O(3)$ Néel field -- is critical instead. The phases are so-named because each realises one of the competing pictures for how the $O(3)$ non-linear sigma model with a topological theta term renormalises to the $\mathfrak{\hat{su}}(2)_1$ Wess-Zumino-Witten model. We support these predictions with density matrix renormalisation group calculations. |
| title | Transition between critical antiferromagnetic phases in the $J_1$-$J_2$ spin chain |
| topic | Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.08095 |