Symmetry-enforced minimal entanglement and correlation in quantum spin chains
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913947505917952 |
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| author | Li, Kangle Zou, Liujun |
| author_facet | Li, Kangle Zou, Liujun |
| contents | The interplay between symmetry, entanglement and correlation is an interesting and important topic in quantum many-body physics. Within the framework of matrix product states, in this paper we study the minimal entanglement and correlation enforced by the $SO(3)$ spin rotation symmetry and lattice translation symmetry in a quantum spin-$J$ chain, with $J$ a positive integer. When neither symmetry is spontaneously broken, for a sufficiently long segment in a sufficiently large closed chain, we find that the minimal Rényi-$α$ entropy compatible with these symmetries is $\min\{ -\frac{2}{α-1}\ln(\frac{1}{2^α}({1+\frac{1}{(2J+1)^{α-1}}})), 2\ln(J+1) \}$, for any $α\in\mathbb{R}^+$. In an infinitely long open chain with such symmetries, for any $α\in\mathbb{R}^+$ the minimal Rényi-$α$ entropy of half of the system is $\min\{ -\frac{1}{α-1}\ln(\frac{1}{2^α}({1+\frac{1}{(2J+1)^{α-1}}})), \ln(J+1) \}$. When $α\rightarrow 1$, these lower bounds give the symmetry-enforced minimal von Neumann entropies in these setups. Moreover, we show that no state in a quantum spin-$J$ chain with these symmetries can have a vanishing correlation length. Interestingly, the states with the minimal entanglement may not be a state with the minimal correlation length. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_20765 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetry-enforced minimal entanglement and correlation in quantum spin chains Li, Kangle Zou, Liujun Strongly Correlated Electrons Quantum Gases Mathematical Physics Quantum Physics The interplay between symmetry, entanglement and correlation is an interesting and important topic in quantum many-body physics. Within the framework of matrix product states, in this paper we study the minimal entanglement and correlation enforced by the $SO(3)$ spin rotation symmetry and lattice translation symmetry in a quantum spin-$J$ chain, with $J$ a positive integer. When neither symmetry is spontaneously broken, for a sufficiently long segment in a sufficiently large closed chain, we find that the minimal Rényi-$α$ entropy compatible with these symmetries is $\min\{ -\frac{2}{α-1}\ln(\frac{1}{2^α}({1+\frac{1}{(2J+1)^{α-1}}})), 2\ln(J+1) \}$, for any $α\in\mathbb{R}^+$. In an infinitely long open chain with such symmetries, for any $α\in\mathbb{R}^+$ the minimal Rényi-$α$ entropy of half of the system is $\min\{ -\frac{1}{α-1}\ln(\frac{1}{2^α}({1+\frac{1}{(2J+1)^{α-1}}})), \ln(J+1) \}$. When $α\rightarrow 1$, these lower bounds give the symmetry-enforced minimal von Neumann entropies in these setups. Moreover, we show that no state in a quantum spin-$J$ chain with these symmetries can have a vanishing correlation length. Interestingly, the states with the minimal entanglement may not be a state with the minimal correlation length. |
| title | Symmetry-enforced minimal entanglement and correlation in quantum spin chains |
| topic | Strongly Correlated Electrons Quantum Gases Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2412.20765 |