Edge Spin fractionalization in one-dimensional spin-$S$ quantum antiferromagnets
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| Format: | Preprint |
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2024
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| _version_ | 1866909635391258624 |
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| author | Kattel, Pradip Tang, Yicheng Pixley, J. H. Andrei, Natan |
| author_facet | Kattel, Pradip Tang, Yicheng Pixley, J. H. Andrei, Natan |
| contents | We show that a gapped spin-$S$ chain with antiferromagnetic (AFM) order exhibits in the thermodynamic limit exponentially localized fractional $\pm \frac{S}{2}$ edge modes when the system possesses U(1) symmetry. We show this for integrable and non integrable spin chains both analytically and numerically. Through exact analytical solutions, we show that an AFM spin-$\frac{1}{2}$ chain with {\it explicitly} broken $\mathbb{Z}_2$ symmetry and an integrable AFM spin-$1$ chain with {\it spontaneously} broken $\mathbb{Z}_2$ symmetry have $\pm \frac{1}{4}$ and $\pm \frac{1}{2}$ fractionalized edge modes, respectively. Furthermore, employing the density matrix renormalization group technique, we extend this analysis to {\it generic} $XXZ-S$ chains with $S\leq 3$ and demonstrate that these fractional spins are robust quantum observables, substantiated by the observation of a variance of the associated fractional spin operators that is consistent with a vanishing functional form in the thermodynamic limit. Moreover, we find that the edge modes are robust to disorder that couples to the Néel order parameter. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_11955 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Edge Spin fractionalization in one-dimensional spin-$S$ quantum antiferromagnets Kattel, Pradip Tang, Yicheng Pixley, J. H. Andrei, Natan Strongly Correlated Electrons Statistical Mechanics Mathematical Physics We show that a gapped spin-$S$ chain with antiferromagnetic (AFM) order exhibits in the thermodynamic limit exponentially localized fractional $\pm \frac{S}{2}$ edge modes when the system possesses U(1) symmetry. We show this for integrable and non integrable spin chains both analytically and numerically. Through exact analytical solutions, we show that an AFM spin-$\frac{1}{2}$ chain with {\it explicitly} broken $\mathbb{Z}_2$ symmetry and an integrable AFM spin-$1$ chain with {\it spontaneously} broken $\mathbb{Z}_2$ symmetry have $\pm \frac{1}{4}$ and $\pm \frac{1}{2}$ fractionalized edge modes, respectively. Furthermore, employing the density matrix renormalization group technique, we extend this analysis to {\it generic} $XXZ-S$ chains with $S\leq 3$ and demonstrate that these fractional spins are robust quantum observables, substantiated by the observation of a variance of the associated fractional spin operators that is consistent with a vanishing functional form in the thermodynamic limit. Moreover, we find that the edge modes are robust to disorder that couples to the Néel order parameter. |
| title | Edge Spin fractionalization in one-dimensional spin-$S$ quantum antiferromagnets |
| topic | Strongly Correlated Electrons Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2406.11955 |