This is an introductory review of the physics of quantum spin liquid states. Quantum
magnetism is a rapidly evolving field, and recent developments reveal that the ground states …

Topological quantum computation has emerged as one of the most exciting approaches to
constructing a fault-tolerant quantum computer. The proposal relies on the existence of …

A spin-1/2 system on a honeycomb lattice is studied. The interactions between nearest
neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of …

This article reviews the physics of high-temperature superconductors from the point of view
of the do** of a Mott insulator. The basic electronic structure of cuprates is reviewed …

BACKGROUND Years ago, Lev Landau taught us how to think about distinct phases of
matter through an order parameter that characterizes the symmetry-broken state relative to …

What are topological phases of matter? First, they are phases of matter at zero temperature.
Second, they have a nonzero energy gap for the excitations above the ground state. Third …

We use the density matrix renormalization group to perform accurate calculations of the
ground state of the nearest-neighbor quantum spin S= 1/2 Heisenberg antiferromagnet on …

We show that quantum systems of extended objects naturally give rise to a large class of
exotic phases—namely topological phases. These phases occur when extended objects …

Over the past several decades, computational approaches to studying strongly-interacting
systems have become increasingly varied and sophisticated. This book provides a …

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 …