TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.1.020
TI  - Symmetry-enforced minimal entanglement and correlation in quantum spin chains
PY  - 2025/07/17
UR  - https://scipost.org/SciPostPhys.19.1.020
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 1
SP  - 020
A1  - Li, Kangle
AU  - Zou, Liujun
AB  - 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-$\alpha$ entropy compatible with these symmetries is $\min\{ -\frac{2}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), 2\ln(J+1) \}$, for any $\alpha∈\mathbb{R}^+$. In an infinitely long open chain with such symmetries, for any $\alpha∈\mathbb{R}^+$ the minimal Rényi-$\alpha$ entropy of half of the system is $\min\{ -\frac{1}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), \ln(J+1) \}$. When $\alpha→ 1$, 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.
ER  -

@Article{10.21468/SciPostPhys.19.1.020,
	title={{Symmetry-enforced minimal entanglement and correlation in quantum spin chains}},
	author={Kangle Li and Liujun Zou},
	journal={SciPost Phys.},
	volume={19},
	pages={020},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.1.020},
	url={https://scipost.org/10.21468/SciPostPhys.19.1.020},
}