Fracton phases of matter represent a frontier in condensed matter physics, introducing exotic gapped quantum orders in three dimensions characterized by subextensive ground state degeneracy and subdimensional excitations.  One route to realizing these orders is through p-loop condensation—a mechanism that transforms decoupled stacks of 2D topological layers into 3D fracton phases.  While lattice fracton models like the X-cube and Ising Cage-Net (ICN) models have been successfully produced via Abelian p-loop condensation, the condensation of non-Abelian p-loops remains an open challenge.  Furthermore, a concrete mechanism for transitions between two distinct, non-trivial fracton orders has remained largely unexplored in the literature.

In this talk, I will present a framework for non-Abelian p-loop, fracton, and planon condensation by constructing extended cage-net models based on the Hu-Geer-Wu (HGW) string-net model.  Using the Ising Cage-Net as an example, I will show how the condensation of non-Abelian $(\sigma\bar{\sigma}, 1)$-loops drives a phase transition into the X-cube model on a truncated cubic lattice.  We will also discuss fracton and planon condensation within cage-net models, which respectively drive the decoupling of the 3D model back to 2D layers or collapse the system into a trivial phase.  Our research establishes a robust Hamiltonian roadmap for the manipulation of spatial dimensions and mobility constraints across the fracton landscape.

Biography

王逸飞，2023年获复旦大学物理系学士学位，现为复旦大学理论物理专业在读博士，导师万义顿教授，研究兴趣是3维分形子序及其与2维拓扑序的联系，有arXiv文章一篇：arXiv:2604.24755。

Inviter: Hao Song