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arXiv 2309.04032cond-mat.stat-mechhep-thquant-ph
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关于对称分辨算符纠缠的更多研究

More on symmetry resolved operator entanglement

Sara Murciano, Jérôme Dubail, Pasquale Calabrese

备注：
26 pages, 6 figures
发表信息：
J. Phys. A: Math. Theor. 57 145002 (2024)
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AI总结：

本文扩展了对称分辨算符纠缠（SROE）的研究，利用共形场论与自由费米子链的解析数值计算，揭示了热密度矩阵遵循算符面积定律、局域算符SROE的对数增长或饱和特性，以及除费米子产生湮灭算符外的纠缠均分现象。

摘要：

量子算符$O$的“算符纠缠”是其复杂度的有用指标，在一维情形下，也是其可由矩阵乘积算符逼近程度的指标。本文聚焦于具有全局$U(1)$守恒定律的自旋链，以及具有确定$U(1)$荷的算符$O$，由此可根据$U(1)$对称性来分辨算符$O$的纠缠。我们采用[PRX Quantum 4, 010318 (2023)]中引入的对称分辨算符纠缠（SROE）概念，并在多个方向上扩展了该文的结果。通过结合共形场论与临界自由费米子链上的精确解析和数值计算，我们研究了热密度矩阵$ρ_β= e^{- βH}$以及在海森堡绘景下演化的带荷局域算符$O = e^{i t H} O e^{-i t H}$的SROE。我们的主要结果为：i) $ρ_β$的SROE遵循算符面积定律；ii) 对于自由费米子，海森堡绘景中的局域算符的SROE可随时间对数增长或饱和至常数值；iii) 除了一对费米子产生和湮灭算符外，所有荷区间内的纠缠均存在均分现象。

英文摘要：

The `operator entanglement' of a quantum operator $O$ is a useful indicator of its complexity, and, in one-dimension, of its approximability by matrix product operators. Here we focus on spin chains with a global $U(1)$ conservation law, and on operators $O$ with a well-defined $U(1)$ charge, for which it is possible to resolve the operator entanglement of $O$ according to the $U(1)$ symmetry. We employ the notion of symmetry resolved operator entanglement (SROE) introduced in [PRX Quantum 4, 010318 (2023)] and extend the results of the latter paper in several directions. Using a combination of conformal field theory and of exact analytical and numerical calculations in critical free fermionic chains, we study the SROE of the thermal density matrix $ρ_β= e^{- βH}$ and of charged local operators evolving in Heisenberg picture $O = e^{i t H} O e^{-i t H}$. Our main results are: i) the SROE of $ρ_β$ obeys the operator area law; ii) for free fermions, local operators in Heisenberg picture can have a SROE that grows logarithmically in time or saturates to a constant value; iii) there is equipartition of the entanglement among all the charge sectors except for a pair of fermionic creation and annihilation operators.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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