Topological insulators are new states of quantum matter which cannot be adiabatically
connected to conventional insulators and semiconductors. They are characterized by a full …

The renormalization group plays an essential role in many areas of physics, both
conceptually and as a practical tool to determine the long-distance low-energy properties of …

This book presents in a pedagogical yet complete way correlated systems in one dimension.
Recent progress in nanotechnology and material research have made one dimensional …

Presenting the physics of the most challenging problems in condensed matter using the
conceptual framework of quantum field theory, this book is of great interest to physicists in …

Decoherence inevitably happens when a quantum state is exposed to its environment,
which can affect quantum critical points (QCPs) in a nontrivial way. As was pointed out in the …

Fractional quantum Hall (FQH) liquids contain extremely rich internal structures which
represent a whole new kind of ordering. We discuss the characterization and classification of …

The existence of fractional charges carrying current is experimentally demonstrated. Using a
2D electron system in a high perpendicular magnetic field we measure the shot noise …

Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon
lowering the energy scale, collective phenomena, bound states, and new effective degrees …

The edge states of the recently proposed quantum spin Hall systems constitute a new
symmetry class of one-dimensional liquids dubbed the “helical liquid,” where the spin …

This tutorial review gives an elementary and self‐contained derivation of the standard
identities (ψη (x)∼ Fη e, etc.) for abelian bosonization in 1 dimension in a system of finite …