Lower Bound to the Entanglement Entropy of the XXZ Spin Ring

条带上XXZ模型液滴态的纠缠熵界

Entanglement Entropy Bounds for Droplet States of the XXZ Model on the Strip

该研究探究条带上海森堡自旋1/2 XXZ模型液滴态纠缠熵的标度行为，分别在无假设和$V$为独立同分布随机变量的条件下，得到带对数修正的面积律与期望面积律。

Entanglement Entropy Bounds in the Higher Spin XXZ Chain

We consider the Heisenberg XXZ spin-$J$ chain ($J\in\mathbb{N}/2$) with anisotropy parameter $Δ$. Assuming that $Δ>2J$, and introducing threshold energies $E_{K}:=K\left(1-\frac{2J}Δ\right)$, we show that the bipartite entanglement entropy (EE) of states belonging to any spectral subspace with energy less than $E_{K+1}$ satisfy a logarithmically corrected area law with prefactor $(2\lfloor K/J\rfloor-2)$. This generalizes previous results by Beaud and Warzel as well as Abdul-Rahman, Stolz and one of the authors, who covered the spin-$1/2$ case.

Bounds on the entanglement entropy of droplet states in the XXZ spin chain

We consider a class of one-dimensional quantum spin systems on the finite lattice $Λ\subset\mathbb{Z}$, related to the XXZ spin chain in its Ising phase. It includes in particular the so-called droplet Hamiltonian. The entanglement entropy of energetically low-lying states over a bipartition $Λ= B \cup B^c$ is investigated and proven to satisfy a logarithmic bound in terms of $\min\lbrace n,\vert B\vert,\vert B^c\vert\rbrace$, where $n$ denotes the maximal number of down spins in the considered state. Upon addition of any (positive) random potential the bound becomes uniformly constant on aver…

Entanglement bounds in the XXZ quantum spin chain

We consider the XXZ spin chain, characterized by an anisotropy parameter $Δ>1$, and normalized such that the ground state energy is $0$ and the ground state given by the all spins up state. The energies $E_K = K(1-1/Δ)$, $K=1,2,\ldots$, can be interpreted as $K$-cluster break-up thresholds for down spin configurations. We show that, for every $K$, the bipartite entanglement of all states with energy below the $(K+1)$-cluster break-up satisfies a logarithmically corrected (or enhanced) area law. This generalizes a result by Beaud and Warzel, who considered energies in the droplet spectrum (i.e.…

Permutation operators, entanglement entropy, and the XXZ spin chain in the limit Δ-> -1

In this paper we develop a new approach to the investigation of the bi-partite entanglement entropy in integrable quantum spin chains. Our method employs the well-known replica trick, thus taking a replica version of the spin chain model as starting point. At each site i of this new model we construct an operator T_i which acts as a cyclic permutation among the n replicas of the model. Infinite products of T_i give rise to local operators, precursors of branch-point twist fields of quantum field theory. The entanglement entropy is then expressed in terms of correlation functions of such operat…

内在噪声与量子纠缠对XXZ海森堡相互作用自旋模型几何和动力学性质的影响

Impacts of Intrinsic Noise and Quantum Entanglement on the Geometric and Dynamical Properties of the XXZ Heisenberg Interacting Spin Model

针对磁场下XXZ海森堡双自旋系统，本文统一分析内在退相干、纠缠、量子态几何距离与速度，并求解含噪量子最速降线及几何相位问题。