KITS-IOP-ITP Joint Seminar
Title: Towards Non-Invertible Anomalies from Generalized Ising Models
Speaker: Dr. Shang Liu (KITP)
Time: Sep. 2 (Friday), 10:00
Place: Rm M830, IOP-CAS
Abstract: 
 The 1d transverse-field Ising model, when projected to the Z2 symmetric sector, is known to have a noninvertible gravitational anomaly that can be compensated by the Z2 toric code model in 2d. In this work, we study the generalization of this type of bulk-boundary correspondence in a large class of qubit lattice models in arbitrary dimensions, called the generalized Ising (GI) models. We provide a systematic construction of exactly solvable bulk models, where the GI models can terminate on their boundaries. In each bulk model, any ground state is robust against local perturbations. If the model has degenerate ground states with periodic boundary condition, the phase is topological and/or fracton ordered. The construction generates abundant examples, including not only prototype ones such as Z2 toric code models in any dimensions no less than two, and the X-cube fracton model, but also more diverse ones such as the Z2 × Z2 topological order, the 4d Z2 topological order with pure-loop excitations, etc. Under a concrete condition, the boundary of the solvable model is anomalous and corresponds to precisely only sectors of the GI model that host certain total symmetry charges and/or satisfy certain boundary conditions. A generalized notion of Kramers-Wannier duality plays an important role in the construction. Also, utilizing the duality, we find an example where a single anomalous theory can be realized on the boundaries of two distinct bulk fracton models, a phenomenon not expected in the case of topological orders.

References: arXiv: 2208.09101

About the speaker: Dr. Shang Liu obtained his PhD in physics at Harvard Unversity in 2021, and is now a Moore postdoctoral fellow at the Kavli Institute for Theoretical Physics at University of California, Santa Barbara. He has broad interests in condensed matter theory, such as topological phases of matter, quantum critical phenomena, entanglement and thermalization, correlated insulators and moire materials.