纠缠与广义朗道范式中的密度矩阵重整化群
Entanglement and the density matrix renormalisation group in the generalised Landau paradigm
AI总结：
本文通过证明纠缠谱简并源于对偶变换中的对称性自发破缺，提出广义密度矩阵重整化群算法，在对偶约束希尔伯特空间上最小化纠缠熵和变分参数，从而提升强关联系统的张量网络模拟效率。
摘要：
纠缠理论和张量网络领域近来已成为刻画物质量子相的核心工具。在本文中，我们确定了有能隙对称量子格点模型基态的纠缠结构，并利用这一结构获得这些基态的最有效张量网络表示。我们通过证明纠缠谱中的简并性源于原始模型到唯一对偶模型的对偶变换来实现这一点，在对偶模型中，整个对偶（广义）对称性被自发破缺，从而不再存在简并性。物理上，该对偶变换相当于对原始基态中未破缺对称性进行（扭曲的）规范场论化。这一结果对使用变分张量网络方法模拟多体系统的复杂性具有深远影响。对于相图中的每个相，完全破缺对称性的基态对偶表示同时最小化纠缠熵和所需变分参数的数量。我们通过开发一种在（对偶）约束希尔伯特空间上运行的广义密度矩阵重整化群算法来展示该思想的适用性，并在一个受扰动的海森堡模型中量化了相对于传统张量网络方法所获得的计算收益。我们的工作证明了广义非可逆对称性及其形式化的范畴论描述对于强关联系统实际模拟的有用性。
英文摘要：
The fields of entanglement theory and tensor networks have recently emerged as central tools for characterising quantum phases of matter. In this article, we determine the entanglement structure of ground states of gapped symmetric quantum lattice models, and use this to obtain the most efficient tensor network representation of those ground states. We do this by showing that degeneracies in the entanglement spectrum arise through a duality transformation of the original model to the unique dual model where the entire dual (generalised) symmetry is spontaneously broken and subsequently no degeneracies are present. Physically, this duality transformation amounts to a (twisted) gauging of the unbroken symmetry in the original ground state. This result has strong implications for the complexity of simulating many-body systems using variational tensor network methods. For every phase in the phase diagram, the dual representation of the ground state that completely breaks the symmetry minimises both the entanglement entropy and the required number of variational parameters. We demonstrate the applicability of this idea by developing a generalised density matrix renormalisation group algorithm that works on (dual) constrained Hilbert spaces, and quantify the computational gains obtained over traditional tensor network methods in a perturbed Heisenberg model. Our work testifies to the usefulness of generalised non-invertible symmetries and their formal category theoretic description for the practical simulation of strongly correlated systems.
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