A lattice realization of general three-dimensional topological order

by Mr Wenjie Xi (The University of Hong Kong)

Tuesday 26 Jul 2022, 13:30 → 14:30 Asia/Shanghai

TDLI Meeting Room N600 (East Wing of Floor 6, North Building)

Abstract

Topological orders (TOs) are a class of phases of matter that extend beyond the Landau symmetry breaking paradigm. The two (spatial) dimensional (2D) TOs have been thoroughly studied. They can be fully classified by a unitary modular tensor category and a chiral central charge cc. A class of 2D TOs with gappable boundaries can be systematically constructed using the Levin--Wen model, whose ground states are string-net condensed states.
Previously, the three (spatial) dimensional (3D) TOs have been classified according to their canonical boundaries, which are described by some unitary fusion 2-categories, 2VecωG2VecGω or an emergent-fermion 2-category. However, no lattice realization of 3D TOs with both canonical and arbitrary boundaries has been reported.
In this paper, we construct a 3D membrane-net model based on a spherical fusion 2-category. The model can be used to systematically study all general 3D TOs with gapped boundaries. The partition function and lattice Hamiltonian of the membrane-net model are constructed using the state sum of the spherical fusion 2-category. We also construct the 3D tube algebra of the membrane-net model to study excitations in the model. We conjecture that all intrinsic excitations in the membrane-net model have a one-to-one correspondence with the irreducible central idempotents of the 3D tube algebra.
We also provide a universal framework to study the mutual statistics of all excitations in 3D TOs using 3D tube algebra. Our approach can be straightforwardly generalized to arbitrary dimensions.

Biography

Mr. Wenjie Xi, the PhD candidate of the University of Hong Kong

Division

Condensed Matter

Other information

Tencent Meeting link: https://meeting.tencent.com/dm/sWY9hdvSV2WC
Meeting ID: 476 954 489                Password: 123456