Topological quantum computation is an important way to do error correcting and Quantum Decoherence-free quantum computation. Condensed matter physics group has achieved a series of results, and was recognized by international community. Two important areas:We have introduced a novel Majorana representation of S=1/2 spins using the Jordan-Wigner transformation and have shown that a generalized spin model of Kitaev defined on a brick-wall lattice is equivalent to a model of non-interacting Majorana fermions with Z2 gauge fields without redundant degrees of freedom. The quantum phase transitions of the system at zero temperature are found to be of topological type and can be characterized by non-local string order parameters (SOP). In appropriate dual representations, these SOP become local order parameters and the basic concept of Landau theory of continuous phase transition can be applied.

Another work is Professor Yu Yue’s deep research on the relationship between gauge invariance of Kitaev model and index theorem in 2+1 dimensions proved by mathematician Xin Chen. The index theorem in even space dimensions plays an important role in physics. But the index theorem in odd space dimensions has not gained enough attention by physicists. This work has for the first time apply index theorem  in odd space dimensions to physics, and proved it played an important role in describing topological sequences of 2+1 dimensions and connecting and cancellation of the boundary and inner topological obstruction. We believe that that this will promote the application of odd space dimensions to physics.

Return to the list