We study the dynamics of the entanglement spectrum, that is the time
evolution of the eigenvalues of the reduced density matrices after a
bipartition of a one-dimensional spin chain. Starting from the ground state of
an initial Hamiltonian, the state of the system is evolved in time with a new
Hamiltonian. We consider both instantaneous and quasi adiabatic quenches of the
system Hamiltonian across a quantum phase transition. We analyse the Ising
model that can be exactly solved and the XXZ for which we employ the
time-dependent density matrix renormalisation group algorithm. Our results show
once more a connection between the Schmidt gap, i.e. the difference of the two
largest eigenvalues of the reduced density matrix and order parameters, in this
case the spontaneous magnetisation.Comment: 16 pages, 8 figures, comments are welcome! Version published in JSTAT
special issue on "Quantum Entanglement In Condensed Matter Physics
