Front dynamics in the XY chain after local excitations

Abstract

We study the time evolution of magnetization and entanglement for initial states with local excitations, created upon the ferromagnetic ground state of the XY chain. For excitations corresponding to a single or two well separated domain walls, the magnetization profile has a simple hydrodynamic limit, which has a standard interpretation in terms of quasiparticles. In contrast, for a spin-flip we obtain an interference term, which has to do with the nonlocality of the excitation in the fermionic basis. Surprisingly, for the single domain wall the hydrodynamic limit of the entropy and magnetization profiles are found to be directly related. Furthermore, the entropy profile is additive for the double domain wall, whereas in case of the spin-flip excitation one has a nontrivial behaviour.

Entanglement spreading after local fermionic excitations in the XXZ chain

“…In summary, our simplistic ansatz (17) provides an interpretation of the excess entropy based on the dispersive dynamics of the quasiparticle modes, where N is the fraction of the initially localized excitation that arrives at the subsystem. In fact, the very same ansatz has recently been suggested for the description of entanglement spreading after local fermionic excitations in the XY chain, finding an excellent agreement with numerics [28]. Note, however, that the XY chain is equivalent to a free-fermion model and thus all the single-particle modes can exactly be included in N .…”

“…The CFT predictions have been tested on the critical transverse Ising [24] and XX chains [25], for various local operators that are lattice analogs of primary or descendant fields. On the other hand, entanglement spreading has also been considered in the non-critical ordered phase of the Ising [26] and XY chains [27,28], starting from a domain-wall initial state excited by a local Majorana operator. Remarkably, the emerging profile of the excess entropy was shown to be captured by a simple probabilistic quasiparticle ansatz [28].…”

“…On the other hand, entanglement spreading has also been considered in the non-critical ordered phase of the Ising [26] and XY chains [27,28], starting from a domain-wall initial state excited by a local Majorana operator. Remarkably, the emerging profile of the excess entropy was shown to be captured by a simple probabilistic quasiparticle ansatz [28]. Indeed, taking into account the dispersive spreading of quasiparticles, only a certain fraction of the initially localized excitation will cross the subsystem boundary located at a certain distance.…”

“…Indeed, taking into account the dispersive spreading of quasiparticles, only a certain fraction of the initially localized excitation will cross the subsystem boundary located at a certain distance. Interpreting this quasiparticle fraction as the probability of finding the excitation within the subsystem, the excess entropy is simply given by a binary expression [28].…”

Subsystem distance after a local operator quench

“…Now we consider the time evolution of a state after a local operator quench in the XY spin chain (in Ref. [55] a similar protocol has been considered in the gapped phase of the XY spin chain). At time t = 0 the spin chain is in the ground state when we insert a local operator at the site j = 0 .…”