Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Solids, Liquids, and Topological Insulators: Symmetry Protected Topological (SPT) Phases of Quantum Matter

Student-Run Research Seminar

Speaker: Michael Ragone, UC Davis
Location: (Online) Zoom
Start time: Thu, Jun 3 2021, 11:00AM

Quantum phases of matter exhibit a richness of structure beyond classical phases: while Landau’s theory dictates that classical phases are governed purely by broken and unbroken symmetries of a model Hamiltonian, quantum phases are distinguished by symmetry and by ``patterns of entanglement’’. Proper formalization of these physical ideas from the condensed matter community and the resultant classification for quantum phases provides a fascinating wide-open mathematical program of research. In this talk, we discuss the classification of 1D Symmetry Protected Topological (SPT) phases of matter, which include topological insulators as an application. The physical conjecture due to Chen-Gu-Wen ’11 has been partially proven by Ogata ’19 for the case of Hamiltonians with translation-invariance and unique gapped ground state. This talk is largely expository and little knowledge of quantum systems is assumed.

Please hold all applause until the end of the talk.