Universal contributions to charge fluctuations in spin chains at finite temperature
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908350845812736 |
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| author | Cai, Kang-Le Cheng, Meng |
| author_facet | Cai, Kang-Le Cheng, Meng |
| contents | At finite temperature, conserved charges undergo thermal fluctuations in a quantum many-body system in the grand canonical ensemble. The full structure of the fluctuations of the total U(1) charge $Q$ can be succinctly captured by the generating function $G(θ)=\left\langle e^{i θQ}\right\rangle$. For a 1D translation-invariant spin chain, in the thermodynamic limit the magnitude $|G(θ)|$ scales with the system size $L$ as $\ln |G(θ)|=-α(θ)L+γ(θ)$, where $γ(θ)$ is the scale-invariant contribution and may encode universal information about the underlying system. In this work we investigate the behavior and physical meaning of $γ(θ)$ when the system is periodic. We find that $γ(θ)$ only takes nonzero values at isolated points of $θ$, which is $θ=π$ for all our examples. In two exemplary lattice systems we show that $γ(π)$ takes quantized values when the U(1) symmetry exhibits a specific type of 't Hooft anomaly with other symmetries. In other cases, we investigate how $γ(θ)$ depends on microscopic conditions (such as the filling factor) in field theory and exactly solvable lattice models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal contributions to charge fluctuations in spin chains at finite temperature Cai, Kang-Le Cheng, Meng Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Quantum Physics At finite temperature, conserved charges undergo thermal fluctuations in a quantum many-body system in the grand canonical ensemble. The full structure of the fluctuations of the total U(1) charge $Q$ can be succinctly captured by the generating function $G(θ)=\left\langle e^{i θQ}\right\rangle$. For a 1D translation-invariant spin chain, in the thermodynamic limit the magnitude $|G(θ)|$ scales with the system size $L$ as $\ln |G(θ)|=-α(θ)L+γ(θ)$, where $γ(θ)$ is the scale-invariant contribution and may encode universal information about the underlying system. In this work we investigate the behavior and physical meaning of $γ(θ)$ when the system is periodic. We find that $γ(θ)$ only takes nonzero values at isolated points of $θ$, which is $θ=π$ for all our examples. In two exemplary lattice systems we show that $γ(π)$ takes quantized values when the U(1) symmetry exhibits a specific type of 't Hooft anomaly with other symmetries. In other cases, we investigate how $γ(θ)$ depends on microscopic conditions (such as the filling factor) in field theory and exactly solvable lattice models. |
| title | Universal contributions to charge fluctuations in spin chains at finite temperature |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2401.09548 |