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

Physical interactions in quantum many-body systems are typically local: Individual
constituents interact mainly with their few nearest neighbors. This locality of interactions is …

We review the dynamics after quantum quenches in integrable quantum spin chains. We
give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the …

We apply unsupervised machine learning techniques, mainly principal component analysis
(PCA), to compare and contrast the phase behavior and phase transitions in several …

A phase transition indicates a sudden change in the properties of a large system. For
temperature-driven phase transitions this is related to nonanalytic behavior of the free …

NATURE abounds with phase transitions. The boiling and freezing of water are everyday
examples of phase transitions, as are more exotic processes such as superconductivity and …

Recent interest in aspects common to quantum information and condensed matter has
prompted a flurry of activity at the border of these disciplines that were far distant until a few …

Entanglement, one of the most intriguing features of quantum theory and a main resource in
quantum information science, is expected to play a crucial role also in the study of quantum …

These notes are the write-up and extension of the lectures I gave over a few years for a class
on “Introduction to Bethe Ansatz” within the Ph. D. program in Statistical Physics at SISSA …

We review recent developments in the physics of ultracold atomic and molecular gases in
optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard …