This is an introductory review of the physics of topological quantum matter with cold atoms.
Topological quantum phases, originally discovered and investigated in condensed matter …

The realization of Bose Einstein condensates (BEC) and quantum degenerate Fermi gases
with cold atoms has been a highlight of quantum physics during the past decade. Cold …

Ultracold quantum gases offer a unique setting for quantum simulation of interacting many-
body systems. The high degree of controllability, the novel detection possibilities and the …

Quantum circuits consisting of random unitary gates and subject to local measurements
have been shown to undergo a phase transition, tuned by the rate of measurement, from a …

The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with
results from exactly solvable models and computational approaches, the concept of bosonic …

Quantum many-body systems divide into a variety of phases with very different physical
properties. The questions of what kinds of phases exist and how to identify them seem hard …

We show that the Haldane phase of S= 1 chains is characterized by a double degeneracy of
the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the …

We discuss the characterization and stability of the Haldane phase in integer spin chains on
the basis of simple, physical arguments. We find that an odd-S Haldane phase is a …

We study the renormalization group flow of the Lagrangian for statistical and quantum
systems by representing their path integral in terms of a tensor network. Using a tensor …

The effect of interactions on topological insulators and superconductors remains, to a large
extent, an open problem. Here, we describe a framework for classifying phases of one …