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Entanglement structure of the two-channel Kondo model

机译：两通道近藤模型的纠缠结构

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摘要

Two electronic channels competing to screen a single impurity spin, as in the two-channel Kondo model, are expected to generate a ground state with a nontrivial entanglement structure. We exploit a spin-chain representation of the two-channel Kondo model to probe the ground-state block entropy, negativity, tangle, and Schmidt gap, using a density matrix renormalization group approach. In the presence of symmetric coupling to the two channels, we confirm field-theory predictions for the boundary entropy difference ln(g_(UV)/g_(IR)) = ln(2)/2 between the ultraviolet and infrared limits and the leading ln(x)/x impurity correction to the block entropy. The impurity entanglement S_(imp) is shown to scale with the characteristic length ξ_(2CK). We show that both the Schmidt gap and the entanglement of the impurity with one of the channels-as measured by the negativity-faithfully serve as order parameters for the impurity quantum phase transition appearing as a function of channel asymmetry, allowing for explicit determination of critical exponents, ν ≈ 2 and β ≈ 0.2. Remarkably, we find the emergence of tripartite entanglement only in the vicinity of the critical channel-symmetric point.
机译：如在两通道近藤模型中一样，两个电子通道竞争筛选单个杂质自旋，有望产生具有非平凡纠缠结构的基态。我们利用密度矩阵重新归一化组方法，利用两通道近藤模型的自旋链表示法来探测基态块的熵，负性，缠结和施密特间隙。在对称耦合到两个通道的情况下，我们确认了场理论预测的紫外和红外极限与前缘之间的边界熵差ln（g_（UV）/ g_（IR））= ln（2）/ 2 ln（x）/ x杂质对块熵的校正。示出了杂质缠结S_（imp）与特征长度ξ_（2CK）成比例。我们显示，通过负性测量，施密特间隙和杂质与沟道之一的纠缠-忠实地充当了杂质量子相变的阶次参数，该杂质量子相变是沟道不对称性的函数，从而可以明确确定临界指数ν≈2和β≈0.2。值得注意的是，我们发现仅在临界通道对称点附近出现了三方纠缠。

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  • 来源
    《Physical review》 |2016年第8期|081106.1-081106.6|共6页
  • 作者

    Bedoor Alkurtass; Abolfazl Bayat; Ian Affleck; Sougato Bose; Henrik Johannesson; Pasquale Sodano; Erik S. Sorensen; Karyn Le Hur;

  • 作者单位

    Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom,Department of Physics and Astronomy, King Saud University, Riyadh 11451, Saudi Arabia;

    Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom;

    Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1;

    Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom;

    Department of Physics, University of Gothenburg, SE-412 96 Gothenburg, Sweden;

    International Institute of Physics, Universidade Federal do Rio Grande do Norte, 59078-400 Natal-RN, Brazil,Departemento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN, Brazil;

    Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1;

    Centre de Physique Theorique, Ecole Polytechnique, CNRS, Universite Paris-Saclay, F-91128 Palaiseau Cedex, France;

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