This INFN Initiative gathers research activities in the interdisciplinary area between Quantum Field Theory, Statistical Physics and Condensed Matter Theory in low dimensions but not only. The traditional methods of exactly solvable models, conformal field theories and integrable systems have been considerably refined in recent years and have remarkably enlarged their range of application, thus leading to a very rich research area. A key feature of these approaches is the ability of solving non-perturbative many-body quantum phenomena that are being observed in recent experiments of mesoscopic quantum devices, cold atom gases and statistical systems out of equilibrium.
Among the developments that boosted the field, let us mention:
i) the increasing number of physical systems where quantum coherent effects are dominant and give rise to new and astonishing behaviours;
ii) the growing interest in understanding the universal features of entanglement and its future applications, among which the attempts at realizing quantum computers;
iii) the possibility of extending the theoretical tools from low dimensions to three space dimensions, as regarding topological effects for example.
Present research projects can be grouped in three broad domains that are deeply interconnected: (a) statistical properties of quantum systems out of equilibrium, (b) measures of entanglement in quantum extended systems, (c) new universality classes and new phases of matter with topological features in two and three space dimensions.

Keywords:
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- integrable quantum field theory
- conformal field theories and universality classes
- extended quantum systems out of equilibrium
- topological quantum field theory
- measures of quantum entanglement

Brownian motion

Conformal map

Dimers

Lattice model

Plane partitions

Quantum quench

S-matrix bootstrap

Topological quantum computation