Séminaire Vanja Marić

We consider translationally invariant quantum spin-1/2 chains with local interactions and a discrete symmetry that is spontaneously broken at zero temperature. We envision experimenters switching off the couplings between two parts of the system and preparing them in independent equilibrium states. One side of the chain settles into a symmetry-breaking ground state and the other side either in equilibrium at higher temperature or out of equilibrium . When the couplings are switched back on, time evolution ensues. We argue that in integrable systems the front separating the ordered region recedes at the maximal velocity of quasiparticle excitations over the ground state. We infer that, generically, the order parameters should vary on a subdiffusive scale of order $t^{1/3}$, where $t$  is time, and their fluctuations should exhibit the same scaling. Thus, the interfacial region exhibits full range correlations, indicating that it cannot be decomposed into nearly uncorrelated subsystems. Using the transverse-field Ising chain as a case study, we demonstrate that all order parameters follow the same universal scaling functions.  Additionally, we present data on Rényi entanglement asymmetries and a prediction valid also in the von Neumann limit. Through an analysis of the skew information, we uncover that the breakdown of cluster decomposition has a quantum contribution: each subsystem within the interfacial region, with extent comparable to the region, exists in a macroscopic quantum state.