| I work with my thesis adviser Prof. Tin-Lun Ho. We have worked on a variety of topics as shown in the following.
Topological superconductor: We studied topological superconductor in 1D, starting from a finite chain with uniformed p-wave interaction. We found that the corresponding mean-field model is not uniformed, and different from the s-wave, the p-wave BCS requires the interactions above a certain threshold. Symmetry enforced quantum spin Hall insulators with pi-flux per plaquette: We have proved under time reversal and magnetic translation symmetry, an insulator with pi-flux per plaquette in 2D must be a quantum spin Hall insulator if it satisfies some certain conditions, regardless of interactions. We also proposed a realization in cold atom. This project is done also in collaboration with Prof. Yuan-Ming Lu. |
Entanglement spectrum: We proposed a new method of calculating entanglement spectrum and its corresponding Schmidt decomposed states in non-interacting fermionic systems. This method reduces the Hilbert space of the problem from exponential growth with subsystem size to linear. Our result shows that by extracting from the entanglement Hamiltonian, one can avoid divergence of the corresponding eigenergies. It also has profound physical meaning, since the temperature is close to zero near quantum mechanical ground states.