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Large classes of quantum scarred Hamiltonians from matrix product states

机译：大类Quantum来自Matrix产品状态的Hamiltonians

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摘要

Motivated by the existence of exact many-body quantum scars in the Affleck-Kennedy-Lieb-Tasaki (AKLT) chain, we explore the connection between matrix product state (MPS) wave functions and many-body quantum scarred Hamiltonians. We provide a method to systematically search for and construct parent Hamiltonians with towers of exact eigenstates composed of quasiparticles on top of an MPS wave function. These exact eigenstates have low entanglement in spile of being in the middle of the spectrum, thus violating the strong eigenstate thermalization hypothesis. Using our approach, we recover the AKLT chain starting from the MPS of its ground state, and we derive the most general nearest-neighbor Hamiltonian that shares the AKLT quasiparticle tower of exact eigenstates. We further apply this formalism to other simple MPS wave functions, and derive families of Hamiltonians that exhibit AKLT-like quantum scars. As a consequence, we also construct a scar-preserving deformation that connects the AKLT chain to the integrable spin-1 pure biquadratic model. Finally, we also derive other families of Hamiltonians that exhibit types of exact quantum scars, including a U(1)-invariant perturbed Potts model.
机译：在Affleck-Kennedy-Lieb-Tasaki（AKLT）链中存在确切的多体量子疤痕的动机，我们探讨了矩阵产品状态（MPS）波函数与许多身体量子疤痕的Hamiltonians之间的连接。我们提供了一种系统地搜索和构建父母汉密尔顿人的父母汉密尔顿人的精确特征塔，由MPS波函数顶部的Quasiply组成。这些精确的特征在频谱中间的桩中具有低缠结，因此违反了强烈的特征热化假设。使用我们的方法，我们从其地面州的MPS开始恢复AKLT链，我们派生了最普遍的最近邻居汉密尔顿人，分享了精确的特征的Aklt Quasiparticle Tower。我们进一步将此形式主义应用于其他简单的MPS波函数，并派生汉密尔顿人的家庭，其展示了Aklt样量子疤痕。因此，我们还构造了一种疤痕保持变形，将AKLT链连接到可集体旋转1纯的双层模型。最后，我们还派生了汉密尔顿人的其他家庭，其展示了精确量子疤痕的类型，包括U（1）-Invariant扰动Potts模型。

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  • 来源
    《Physical review》 |2020年第8期|085120.1-085120.19|共19页
  • 作者

    Sanjay Moudgalya; Edward OBrien; B. Andrei Bernevig; Paul Fendley; Nicolas Regnault;

  • 作者单位

    Department of Physics Princeton University Princeton New Jersey 08544 USA;

    Rudolf Peierls Centre for Theoretical Physics Clarendon Laboratory Parks Road Oxford OX1 3PU England United Kingdom;

    Department of Physics Princeton University Princeton New Jersey 08544 USA;

    Rudolf Peierls Centre for Theoretical Physics Clarendon Laboratory Parks Road Oxford OX1 3PU England United Kingdom All Souls College Oxford OX1 4AL England United Kingdom;

    Department of Physics Princeton University Princeton New Jersey 08544 USA Laboratoire de Physique de l' Ecole Normale Superieure ENS Universite PSL Centre National de la Recherche Scientifique Sorbonne Universite Universite Paris-Diderot Sorbonne Paris Cite Paris France;

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