论文标题
来自Matrix产品状态
Large Classes of Quantum Scarred Hamiltonians from Matrix Product States
论文作者
论文摘要
由于AKLT链中存在确切的多体量子疤痕的动机，我们探索了矩阵乘积状态（MPS）波函数与多体量子疤痕的哈密顿量之间的联系。我们提供了一种系统地搜索和构建父母哈密顿量的方法，该塔是由MPS波函数顶部的精确本征塔组成的精确征收的塔。尽管处于频谱中间，但这些确切的本征态仍具有较低的纠缠，因此违反了强征征热假说（ETH）。使用我们的方法，我们从基地状态的国会议员开始恢复AKLT链，并得出了最接近的最近邻居汉密尔顿，该汉密尔顿共享了Eigenstates的Aklt Quasiparticle塔。我们进一步将这种形式主义应用于其他简单的MPS波函数，并得出了表现出类似Aklt的量子疤痕的新哈密顿家族。结果，我们还构建了一个疤痕的变形，将AKLT链连接到可集成的Spin-1纯生物段模型。最后，我们还推出了其他汉密尔顿家族的家庭，这些家庭表现出新型的精确量子疤痕，包括$ u（1）$ - 不变的扰动Potts模型。
Motivated by the existence of exact many-body quantum scars in the AKLT chain, we explore the connection between Matrix Product State (MPS) wavefunctions 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 wavefunction. These exact eigenstates have low entanglement in spite of being in the middle of the spectrum, thus violating the strong Eigenstate Thermalization Hypothesis (ETH). 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 wavefunctions, and derive new 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 new types of exact quantum scars, including a $U(1)$-invariant perturbed Potts model.
