Local quenches on quantum many body systems

Abstract

In this thesis we have studied local quenches on quantum many body systems. We have investigated the variation of von Neumann entropy of subsystem reduced states of general many-body lattice spin systems due to local quantum quenches. We obtained Lieb-Robinson like bounds that are independent of the subsystem volume. More specifically, the bound exponentially increases with time but exponentially decreases with the distance between the subsystem and the region where the quench takes place. The fact that the bounds are independent of the subsystem volume leads to stronger constraints (than previously known) on the propagation of information throughout many-body systems. In particular, it shows that bipartite entanglement satisfies an effective ¿light cone¿, regardless of system size. A particular model for a quantum many body system is the quantum Ising model. We have found a new phenomenon for it, which we have called shielding property. Namely, suppose that the state of the system is the Gibbs state and that the field in one particular site is null, then whatever the fields on each spin and exchange couplings between neighbouring spins are, the reduced states of the subchains to the right and to the left of this site are exactly the Gibbs states of each subchain alone. Therefore, even if there is a strong exchange coupling between the extremal sites of each subchain, the Gibbs states of the each subchain behave as if there is no interaction between them. In general, if a lattice can be divided into two disconnected regions separated by an interface of sites with zero applied field, we can guarantee the same result if the surface contains a single site. When there are more sites in the interface, the system satisfies the shielding property for the ground state under some conditions. We show that one particular situation where the system satisfies these required conditions is when it is frustration free.