We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.

Dynamical phase transitions can occur in isolated quantum systems that are brought out of equilibrium by sudden parameter changes. We discuss the characterization of such dynamical phase transitions based on the statistics of produced excitations. We consider both the O(N) model in the large N limit and a spin model with long range interactions and show that the dynamical criticality of their prethermal steady-states manifests most dramatically not in the average number of excitations but in their higher moments. We argue that the growth of defect fluctuations carries unique signatures of the dynamical criticality, irrespective of the precise details of the model. Our theoretical results should be relevant to quantum quench experiments with ultracold bosonic atoms in optical lattices.

We study the statistics of the work done by globally changing in time with a generic protocol the mass in a free bosonic field theory with relativistic dispersion and the transverse field in the one-dimensional Ising chain both globally and locally. In the latter case we make the system start from the critical point and we describe it in the scaling limit. We provide exact formulas in all these cases for the full statistics of the work and we show that the low-energy part of the distribution of the work displays an edge singularity whose exponent does not depend on the specifics of the protocol that is chosen and may only depend on the position of the initial and final values with respect to the critical point of the system. We also show that the condensation transition found in the bosonic system for sudden quenches [A. Gambassi and A. Silva, Phys. Rev. Lett. 109, 250602 (2012)] is robust with respect to the choice of the protocol.