扭结激发的纠缠内容

Density matrix of electrons coupled to phonons and the electron-phonon entanglement content of excited states

We derive the exact reduced density matrix for the electrons in an analytically solvable electron-phonon model. Here, the electrons are described as a Luttinger liquid that is coupled to Einstein phonons. We further derive analytical expressions for the electron-phonon entanglement, its spectrum and mutual information at finite and zero temperature as well as for excited states. The entanglement entropy is additive in momentum for the quasi-particle excited states, but not in the electron-phonon coupled eigenmodes of the system.

Anyonic Entanglement and Topological Entanglement Entropy

We study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a particular form of entanglement that does not exist in conventional quantum mechanical systems. We study this entanglement by adapting standard notions of entropy to anyonic systems. We use the algebraic theory of anyon models (modular tensor categories) to illustrate the nonlocal entanglement structure of anyonic systems. Using this formalism, we present a gen…

量子伊辛模型中量子相变的动力学

Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model

一维量子伊辛模型是量子相变的一个精确可解的例子。我们研究其行为在淬火过程中从顺磁性铁磁相所造成的横向场逐渐关闭，在一个固定的速率，其特征在于淬火时间$τ_Q$。与Kibble-Zurek机制一致，跃迁后系统的量子态呈现出特征关联长度$\hatξ$，与猝灭时间$τ_Q$的平方根成正比.该相关长度的倒数决定了转变后缺陷的平均密度。在本文中，我们表明，$\hatξ$也控制着一块$L$自旋与其余系统的纠缠熵。对于大的$L$，这个熵在$\frac16\log_2\hatξ$处饱和，正如从Kibble-Zurek机制所预期的那样。接近临界点时，熵饱和时，块大小$L\approx\hatξ$，但-在随后的演变中的铁磁相-一个稍大的长度尺度$l=\sqrt{τ_Q}\lnτ_Q$发展作为量子退相的结果，和熵饱和时，$L\approx l$。我们还研究了自旋-自旋关联。我们发现，接近临界点的铁磁相关指数衰减的动力学相关长度$\hatξ$，但在以下的演变这关联函数变得振荡的距离小于这个规模。然而，这些振荡的波长和相关长度仍然由$\hatξ$决定。我们还推导出了有限自旋链在跃迁后扭结数的概率分布。

Entanglement entropy after a partial projective measurement in $1+1$ dimensional conformal field theories: exact results

We calculate analytically the Rényi bipartite entanglement entropy $S_α$ of the ground state of $1+1$ dimensional conformal field theories (CFT) after performing a projective measurement in a part of the system. We show that the entanglement entropy in this setup is dependent on the central charge and the operator content of the system. When the measurement region $A$ separates the two parts $B$ and $\bar{B}$, the entanglement entropy between $B$ and $\bar{B}$ decreases like a power-law with respect to the characteristic distance between the two regions with an exponent which is dependent on t…

Lattice regularisation and entanglement structure of the Gross-Neveu model

We construct a Hamiltonian lattice regularisation of the $N$-flavour Gross-Neveu model that manifestly respects the full $\mathsf{O}(2N)$ symmetry, preventing the appearance of any unwanted marginal perturbations to the quantum field theory. In the context of this lattice model, the dynamical mass generation is intimately related to the Coleman-Mermin-Wagner and Lieb-Schultz-Mattis theorem. In particular, the model can be interpreted as lying at the first order phase transition line between a trivial and symmetry-protected topological (SPT) phase, which explains the degeneracy of the elementar…

在共形场论中的测量诱导纠缠

Measurement-Induced Entanglement in Conformal Field Theory

研究测量对多体纠缠的影响，揭示Tomonaga-Luttinger液体中测量诱导纠缠的普遍性与共形不变性，通过复制技巧计算其精确值。

具有平方反比统计相互作用的自旋系统中的纠缠

Entanglement in a spin system with inverse square statistical interaction

利用分数阶统计方法研究了具有有效基本自由度的系统的基态纠缠度。为此，我们明确地构建了一个链的$N$自旋与平方反比相互作用（Haldane-Shastry模型）在外部均匀磁场的存在下的基态。对于这样一个零温系统，我们计算了有限尺寸和热力学极限下的基态纠缠。我们将量子关联的行为与发生在饱和场中的自旋凝聚现象联系起来。

量子点基纳米结构中限制势几何对纠缠的影响

Effect of confinement potential geometry on entanglement in quantum dot-based nanostructures

我们计算了两个电子之间的空间纠缠被困在纳米结构的一个广泛的类的限制势，包括单，双量子点，和核-壳量子点结构。通过使用参数化的禁闭势，我们能够从一种结构切换到其他的连续性，并分析如何纠缠的影响，在禁闭几何的变化。我们计算的多体波函数的时间无关的薛定谔方程的“精确”对角化。我们讨论了纠缠度与波函数的特定切割之间的关系，并表明，在一个单一的高度对称点的波函数可以是一个很好的指示系统的纠缠内容。我们分析了空间纠缠和库仑相互作用之间违反直觉的关系，它将前者的最大值（最小值）连接到后者的最小值（最大值）。我们引入了一个潜在的量子相变，它涉及量子态特征不同的空间拓扑结构。最后，我们表明，通过改变形状，范围和强度的限制势，它是可能的诱导强烈和快速变化的两个电子之间的纠缠。该性质可用于根据特定应用所需的缠结水平来定制纳米结构。

纠缠谱有多普遍？

How universal is the entanglement spectrum?

现在普遍认为，基态纠缠谱（ES）表现出一个给定相位的普遍特征。在这封信中，我们表明这种信念一般是错误的。最重要的是，我们表明，纠缠哈密顿量可以进行量子相变，其中它的基态和低能谱表现出奇异的变化，即使当物理系统保持在相同的相位。对于对称性破缺问题，这意味着ES和Renyi熵可以完全误导，而对于量子霍尔系统，ES具有比迄今为止假设的更少的普遍内容。

Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state

We study a class of periodically driven $d-$dimensional integrable models and show that after $n$ drive cycles with frequency $ω$, pure states with non-area-law entanglement entropy $S_n(l) \sim l^{α(n,ω)}$ are generated, where $l$ is the linear dimension of the subsystem, and $d-1 \le α(n,ω) \le d$. We identify and analyze the crossover phenomenon from an area ($S \sim l^{ d-1}$ for $d\geq1$) to a volume ($S \sim l^{d}$) law and provide a criterion for their occurrence which constitutes a generalization of Hastings' theorem to driven integrable systems in one dimension. We also find that $S_n…

无隙对称保护拓扑态中的普适纠缠谱

Universal entanglement spectrum in gapless symmetry protected topological states

该研究结合场论与数值方法计算一维无隙对称保护拓扑态的纠缠谱，发现其兼具边缘简并与边界共形场论算符信息，还识别出新型对称增强共形边界条件。

Magnetic field-dependent dynamics and field-driven metal-to-insulator transition of the half-filled Hubbard model: A DMFT+DMRG study

We study the magnetic field driven metal-to-insulator transition in half-filled Hubbard model on the Bethe lattice, using the dynamical mean-field theory by solving the quantum impurity problem with density-matrix renormalization group algorithm. The method enables us to obtain a high-resolution spectral densities in the presence of a magnetic field. It is found that the Kondo resonance at the Fermi level splits at relatively high magnetic field: the spin-up and spin-down components move away from the Fermi level and finally form a spin polarized band insulator. By calculating the magnetizatio…

一维Kugel-Khomskii模型的纠缠熵和谱

Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model

我们研究了一维Kugel-Khomskii模型中自旋和轨道自由度的量子纠缠，该模型包括无隙和有隙两种相位，采用分析技术和精确对角化方法，最多可达16个位置.我们计算的纠缠熵，纠缠谱使用各种分区或“削减”的希尔伯特空间，包括两个不同的实空间削减和动量空间削减。我们的结果表明，Kugel-Khomski模型具有一些新的功能，以前没有遇到的纠缠谱的研究。值得注意的是，我们发现强大的差距，在纠缠谱的有隙和无隙阶段的轨道分区，并显示这些是不连接到彼此。我们观察到的计数的低位纠缠本征值表明，“虚边”的图片，相当于低能量的哈密顿量的虚边，这里的一个无间隙的腿的两条腿的梯子，到“低能量”纠缠哈密顿量的故障为这个模型，即使等价已被证明持有类似的削减在一大类密切相关的模型。此外，我们表明，动量空间削减在无隙相位导致纠缠谱的定性差异相比，相同的削减在无隙自旋1/2海森堡自旋链。与纠缠熵相比，我们强调了纠缠谱中新的信息含量，并利用量子纠缠给出了模型的精细相图。使用分析参数，利用各种对称性的模型，并应用参数的绝热连续性从两个完全可解的点的模型，我们也能够证明几个结果的结构的低位纠缠本征值。