Quantum spin chains appear ubiquitously in modern physics from statistical physics to the AdS/CFT duality. In the scaling limit, they can be described by two-dimensional quantum field theories. The non-perturbative bootstrap program provides exact results to observables in the critical points and their integrable perturbations. Away from these special cases, approximate methods can be used. Recent experiments showed, that quantum spin chains can be realized in various settings, moreover, it is possible to tune their parameters to bring them to regimes where the scaling field theory applies. Therefore, exact and approximate predictions of the scaling field theory and their validity in the spin chains are of great interest. Using existing machinery and developing new numerical and analytic methods we shall explore the scaling region of quantum spin chains, provide and verify predictions of scaling field theories.

The specific goals of the project include:

- Identification and interpretation of quasi-particle excitations in non-equilibrium settings

- Dynamical properties of quantum spin chains in the scaling limit

- Non-perturbative phenomena, such as confinement and false vacuum decay

- Identification of non-trivial critical points