D´epartement de physique, Universit´e de Sherbrooke,
Title: The Landau paradigm and beyond: An essay on the synthesis
The main goal of the presentation is to give an accessible overview of the recent research
focused mainly on the quantum phase transitions with non-conventional orders, such that
the textbook theory, known also as the Landau paradigm, does not work in a usual way. After
a brief reminder of the Landau theory, we will use the simple well-known solvable quantum
chain model to explain the key points of the generalized unifying approach to treat the
critical phenomena with local and topological orders. A non-technical account of the results
of the theory applied for several chain and ladder models will be given. These models of
quantum spins or fermions manifest distinct exotic topological orders, quantified by the
string/brane order parameters. The phase transitions of different types, disentanglement,
and additional attributes of topological order such as winding numbers and edge Majoranas,
are shown to be related to the properties of zeros of the partition function.
The main message is that the extended Landau theory, crucially amended by duality and
spontaneous breaking of hidden symmetry, remains instrumental even for non-conventional
orders. The local and non-local order parameters are related by duality, and probing a phase
transition and related emerging order is a problem of appropriate choice of variables.
New directions and applications of the theory will be also discussed.