Boundary Hamiltonian Approach to Gapped Topological Phases on Open Surfaces
报告人:
Yong-Shi Wu 吴咏时
Distinguished Professor Department of Physics and Astronomy, University of Utah
报告时间:
2017-10-20 15:30
报告地点:
Conference Hall 322, Science Building, Tsinghua University
主办单位:
高等研究院
简介:
To study gapped?topological phases on??open?surfaces with boundary, we propose to add appropriately constructed boundary terms in the?Hamiltonian. Our setting is exactly solvable discrete models, such as string-net models (andWitten-Dijkgraaf models). The full Hamiltonian?in our approach yields a topologically protected, gapped energy spectrum, with the corresponding?wave functions robust under topology-preserving transformations of the lattice.We explicitly?present the wavefunctions of the ground states and boundary elementary excitations, as well as creation and hopping operators of boundary?quasi-particles. We find that given?a bulk topological?order, the gapped boundary conditions?are?described by Frobenius algebras in?its input data.?Emergent topological properties of the ground states?and boundary excitations are?described?by (bi-) modules over Frobenius algebras.
