CPM Seminar

How to make the Landau framework for topological order:
Introduction to the recipe book

Gennady Chitov

Laurentian University

The main result to be emphasised is the proposed framework unifying the Landau paradigm with the concept of topological order. To explain how the Landau theory can be extended to accommodate nonconventional orders I will present analysis of quantum phase transitions in several chain and ladder models. The chain models are exactly solvable, while the ladders are dealt within a mean-field approximation. The distinct gapped phases of these models are described by nonlocal string order parameters (SOPs) which are calculated analytically. The phases are also classified according to their hidden broken symmetries. By utilizing duality transformations we map the SOPs onto local order parameters in some dual representation. Thus the local and nonlocal orders related by duality become a matter of convenient choice of variables of the Hamiltonian. I will explain how this uni- fied framework can be applied to other systems, e.g., topological insulators and superconductors. Directions of the future work will be also discussed.