Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group
Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group
复制标题
谱分岔重整群的多体定域系统纠缠全息映射
DOI：
10.1103/physrevb.93.104205
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发表时间：
2015
影响因子：
3.7
通讯作者：
Cenke Xu
中科院分区：
文献类型：
--
作者：
Yi;X. Qi;Cenke Xu
我们引入谱分岔重整化群（SBRG）作为多体定域（MBL）系统实空间重整化群的推广，而不截断希尔伯特空间。从完整 MBL 阶段的无序多体哈密顿量开始，SBRG 流向 MBL 定点哈密顿量，并生成所有本征态的局部守恒量和矩阵乘积状态表示。该方法适用于所有维度的任何晶格上具有任意相互作用强度的自旋模型和费米子模型，只要模型处于 MBL 相。我们特别关注具有强无序性的 $1d$ 相互作用的马约拉纳链，并使用纠缠熵绘制其相图。 SBRG 流还生成纠缠全息映射，将 MBL 状态双重化为装饰有小黑洞的碎片全息空间。
We introduce the spectrum bifurcation renormalization group (SBRG) as a generalization of the real-space renormalization group for the many-body localized (MBL) system without truncating the Hilbert space. Starting from a disordered many-body Hamiltonian in the full MBL phase, the SBRG flows to the MBL fixed-point Hamiltonian, and generates the local conserved quantities and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the MBL phase. In particular, we focus on the $1d$ interacting Majorana chain with strong disorder, and map out its phase diagram using the entanglement entropy. The SBRG flow also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space decorated with small blackholes.