Deconfined criticality and a gapless $\mathbb{Z}_2$ spin liquid in the square lattice antiferromagnet
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arXiv
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| Formato: | Preprint |
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2021
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| _version_ | 1866914026603151360 |
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| author | Shackleton, Leyna Thomson, Alex Sachdev, Subir |
| author_facet | Shackleton, Leyna Thomson, Alex Sachdev, Subir |
| contents | The theory for the vanishing of Néel order in the spin $S=1/2$ square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the $J_1$-$J_2$ model): a gapless spin liquid is present for a narrow window of parameters between the vanishing of the Néel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable $\mathbb{Z}_2$ spin liquid with massless Dirac spinon excitations; on the other side the critical point, the SU(2) spin liquid (the `$π$-flux' phase) is presumed to be unstable to confinement to the Néel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant, and weakly breaks the SO(5) symmetry which rotates between the Néel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless $\mathbb{Z}_2$ spin liquid; on the other side of the critical point, the U(1) spin liquid (the `staggered flux' phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent $z \neq 1$, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing $J_2/J_1$: Néel, gapless $\mathbb{Z}_2$ spin liquid, and valence bond solid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_09537 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Deconfined criticality and a gapless $\mathbb{Z}_2$ spin liquid in the square lattice antiferromagnet Shackleton, Leyna Thomson, Alex Sachdev, Subir Strongly Correlated Electrons High Energy Physics - Theory The theory for the vanishing of Néel order in the spin $S=1/2$ square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the $J_1$-$J_2$ model): a gapless spin liquid is present for a narrow window of parameters between the vanishing of the Néel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable $\mathbb{Z}_2$ spin liquid with massless Dirac spinon excitations; on the other side the critical point, the SU(2) spin liquid (the `$π$-flux' phase) is presumed to be unstable to confinement to the Néel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant, and weakly breaks the SO(5) symmetry which rotates between the Néel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless $\mathbb{Z}_2$ spin liquid; on the other side of the critical point, the U(1) spin liquid (the `staggered flux' phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent $z \neq 1$, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing $J_2/J_1$: Néel, gapless $\mathbb{Z}_2$ spin liquid, and valence bond solid. |
| title | Deconfined criticality and a gapless $\mathbb{Z}_2$ spin liquid in the square lattice antiferromagnet |
| topic | Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2104.09537 |