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arXiv 2007.10380cond-mat.str-elcond-mat.stat-mechquant-ph
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拟对称群与多体疤痕动力学

Quasi-symmetry groups and many-body scar dynamics

Jie Ren, Chenguang Liang, Chen Fang

摘要:

在量子系统中,由哈密尔顿算子的简并本征向量所张成的子空间可能具有比哈密尔顿算子本身更高的对称性。当这个增强对称群可以由局部算子生成时,我们称之为拟对称群。当群是李群时,耦合到准对称群的某些生成元的外场提升了简并性,并导致简并子空间内的精确周期动力学,即多体疤痕动力学(假设哈密顿量是不可积的)。我们提供了两个相关的计划,用于构建一维自旋模型具有按需准对称群,与精确的周期性演化的预选产品或矩阵产品状态下一定的外部领域。

英文摘要:

In quantum systems, a subspace spanned by degenerate eigenvectors of the Hamiltonian may have higher symmetries than those of the Hamiltonian itself. When this enhanced-symmetry group can be generated from local operators, we call it a quasi-symmetry group. When the group is a Lie group, an external field coupled to certain generators of the quasi-symmetry group lifts the degeneracy, and results in exactly periodic dynamics within the degenerate subspace, namely the many-body-scar dynamics (given that Hamiltonian is non-integrable). We provide two related schemes for constructing one-dimensional spin models having on-demand quasi-symmetry groups, with exact periodic evolution of a pre-chosen product or matrix-product state under certain external fields.

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