BIMSA > YMSC-BIMSA Quantum Information Seminar Topological Orders from Frustration-free Hamiltonians with Reflection Positivity
Topological Orders from Frustration-free Hamiltonians with Reflection Positivity
Organizers
Song Cheng , Jinpeng Liu , Zhengwei Liu , Ziwen Liu
Speaker
Zishuo Zhao
Time
Friday, December 5, 2025 4:00 PM - 5:30 PM
Venue
Shuangqing-B627
Online
Zoom 230 432 7880 (BIMSA)
Abstract
We establish a framework with reflection positivity as the first principle to study topologically ordered quantum spin systems. For any reflection positive frustration-free Hamiltonian, we proved that the local topological quantum order (LTQO) condition of ground states on a disk holds if and only if the ground state on the sphere is non-degenerate. Furthermore, we show that the Osterwalder-Schrader reconstruction produces the boundary local net of operator algebras. Interestingly, the modular group generated by the entanglement Hamiltonian of the ground state factorizes when restricted to the boundary algebras. The talk is based on the joint work with Zhengwei Liu (arXiv:2510.20662).