Wegner-Wilson loops in string nets

Bulk Geometry of the Many Body Localized Phase from Wilson-Wegner Flow

Tensor networks are a powerful formalism for transforming one set of degrees of freedom to another. They have been heavily used in analyzing the geometry of bulk/boundary correspondence in conformal field theories. Here we develop a tensor-network version of the Wilson-Wegner Renormalization Group Flow equations to efficiently generate a unitary tensor network which diagonalizes many-body localized Hamiltonians. Treating this unitary tensor network as a bulk geometry, we find this emergent geometry corresponds to the shredded horizon picture: the circumference of the network shrinks exponentia…

Fixed points of Wegner-Wilson flows and many-body localization

Many-body localization (MBL) is a phase of matter that is characterized by the absence of thermalization. Dynamical generation of a large number of local quantum numbers has been identified as one key characteristic of this phase, quite possibly the microscopic mechanism of breakdown of thermalization and the phase transition itself. We formulate a robust algorithm, based on Wegner Wilson flow (WWF) renormalization, for computing these conserved quantities and their interactions. We present evidence for the existence of distinct fixed point distributions of the latter: a flat "white noise" dis…

Tensor-network approach to phase transitions in string-net models

We use a recently proposed class of tensor-network states to study phase transitions in string-net models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops expectation values, and a natural order parameter detecting the breakdown of the topological phase. In the presence of a string tension, a quantum phase transition occurs between the topological phase and a trivial phase. We benchmark our approach for $\mathbb{Z}_2$ string nets and capture the second-order phase transition which is well known from the exact mapp…

有限温度下包含所有任意子的扩展弦网模型

Extended string-net models with all anyons at finite temperature

本文研究扩展弦网模型在有限温度下的拓扑序稳定性，通过精确配分函数和光谱简并度计算，发现热力学极限下任意非零温度均破坏拓扑序，而有限尺寸系统中拓扑序可存活至有限温度，并揭示了类似一维经典 Ising 模型的温度-尺寸标度关系。