Luo, Zhu-Xi - Harvard University

Gapped interfaces in fracton models and foliated fields

This work investigates the gapped interfaces of foliated field theories that describe fracton phases of matter, focusing on the X-cube model as an example. We analyze the gapped interfaces between X-cube and the vacuum (gapped boundary), 3+1D toric code, and another X-cube model. The interfaces can be either undecorated or decorated, with the latter involving adding $K$-matrix Chern-Simons type terms to specific undecorated interfaces. We systematically identify the undecorated interfaces for the aforementioned cases and explore general decorations, supported by many examples. We further demonstrate the formulation of lattice models for the general gapped interfaces found in foliated field theories and present several illustrative instances. While previous literature has discussed the gapped boundaries of the X-cube model, our formalism facilitates the straightforward establishment of new decorated boundaries. This work is a collaboration with Po-Shen Hsin and Ananth Malladi.