Microscopic models of (3+1)D Borromean-Rings topological order

by Dr Peng Ye(叶鹏) (Sun Yat-Sen University)

Wednesday 18 Mar 2026, 10:30 → 11:30 Asia/Shanghai

Tsung-Dao Lee Institute/N4F-N400 - meeting room (Tsung-Dao Lee Institute)

Host: Prof. Xin Liu  

Venue: TDLI Meeting Room N400

Tencent Meeting link: https://meeting.tencent.com/dm/F9mnkMeBbmbT 

Meeting ID: 935763949, no password

 

Abstract:

Continuum field-theoretical descriptions of topological order at long distances, philosophically similar to Ginzburg–Landau field theory for symmetry-breaking phases, are guided by a small set of fundamental principles such as gauge invariance, locality, symmetry considerations, expected response, and topological invariance. Without explicit reference to microscopic realizations at short distances, the physical relevance and microscopic realizability of these continuum field theories are often questioned. The (3+1)D Borromean-Rings topological order was introduced by Chan, Ye, Ryu (PRL 2018) via a topological field theory of BF+AAB type. The unique feature is that there is a nontrivial braiding phase accumulated after a braiding process in which two loop excitations and one particle’s closed trajectory form a Borromean rings. However, the long-standing skepticism about its physical relevance and microscopic realizability persists over the past years. In this talk, I will present the microscopic construction of the field theory and show that D_4 quantum double model is the lattice realization of the BF+AAB field theory with gauge group (Z_2)^3. After constructing creation operators of excitations, we compute fusion, shrinking, quantum dimensions, and verify fusion-shrinking consistency relations, all of which perfectly agree with the results from field theory. Future work include further exploration of microscopic study of fusion pentagon equations and shrinking-fusion hexagon equations previously predicted by field theory.

 

References:

arXiv:2512.21148.

 

Biography:

Peng Ye is currently a professor at the School of Physics, Sun Yat-sen University (since August 2018), Guangzhou. His primary field of research is quantum many-body theory. He earned his B.Sc. in Physics from Sun Yat-sen University in July 2007 and completed his PhD at the Institute for Advanced Study of Tsinghua University in July 2012. From September 2012 to August 2015, he worked as a postdoctoral researcher at the Perimeter Institute for Theoretical Physics in Canada. He then became a postdoctoral research associate and Gordon & Betty Moore fellow at of the Anthony J. Leggett Institute for Condensed Matter Theory and Department of Physics at the University of Illinois at Urbana-Champaign, USA, from August 2015 to August 2018. He currently serves as a member of Editorial Board of Physical Review Research of the American Physical Society.