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Chinese Physics Letters

General Properties of Thermal Entanglement in an Arbitrary-Length Heisenberg Spin Chain

张婷, 吴伟, 陈平形, 李承祖

Published Jan 1, 2007• 0 citations
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Abstract

我们基于它的 eigenstates 的分类在 arbitary-length1D 海森堡 spin-1/2 链调查热纠纷的一般性质。纠纷上的磁场和温度的影响是讨论的品质上，三个特征被介绍。结论为由两部组成、多国参加的纠纷成立，并且与 Arnesen 等数字地证明的结果一致。

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We study the infinite-temperature properties of an infinite sequence of random quantum spin chains using a real-space renormalization group approach, and demonstrate that they exhibit nonergodic behavior at strong disorder. The analysis is conveniently implemented in terms of SU(2)_{k} anyon chains that include the Ising and Potts chains as notable examples. Highly excited eigenstates of these systems exhibit properties usually associated with quantum critical ground states, leading us to dub them "quantum critical glasses." We argue that random-bond Heisenberg chains self-thermalize and that the excited-state entanglement crosses over from volume-law to logarithmic scaling at a length scale that diverges in the Heisenberg limit k→∞. The excited state fixed points are generically distinct from their ground state counterparts, and represent novel nonequilibrium critical phases of matter.
一个三纺纱的 XXZ 海森堡链 withthree 纺纱相互作用的纠纷性质借助于对的同时发生被学习明智。纠纷。我们显示出 thatground 状态对明智的纠纷，对明智的热纠纷，或量阶段转变不是在反的现在铁磁性的旋转链。为铁磁性的盒子，量阶段转变在 1 当 J/T 的价值增加时，明智的热纠纷增加的三纺纱的联合力量，和对并且与各向异性的相互作用和三纺纱的相互作用减少为各向异性的相互作用并且在一些珍视的Δ = 发生。另外，我们发现那增加各向异性的相互作用和三纺纱的相互作用愿望减少批评温度。
We investigate the eigenstate thermalization hypothesis (ETH) in integrable models, focusing on the $\text{spin}\ensuremath{-}\frac{1}{2}$ isotropic Heisenberg (XXX)(XXX)(XXX) chain. We provide numerical evidence that the ETH holds for typical eigenstates (weak ETH scenario). Specifically, using a numerical implementation of state-of-the-art Bethe ansatz results, we study the finite-size scaling of the eigenstate-to-eigenstate fluctuations of the reduced density matrix. We find that fluctuations are normally distributed, and their standard deviation decays in the thermodynamic limit as ${L}^{\ensuremath{-}1/2}$, with LLL the size of the chain. This is in contrast with the exponential decay that is found in generic nonintegrable systems. Based on our results, it is natural to expect that this scenario holds in other integrable spin models and for typical local observables. Finally, we investigate the entanglement properties of the excited states of the XXXXXXXXX chain. We numerically verify that typical midspectrum eigenstates exhibit extensive entanglement entropy (i.e., volume-law scaling).