2 research outputs found
Entanglement and alpha entropies for a massive Dirac field in two dimensions
We present some exact results about universal quantities derived from the
local density matrix, for a free massive Dirac field in two dimensions. We
first find the trace of powers of the density matrix in a novel fashion, which
involves the correlators of suitable operators in the sine-Gordon model. These,
in turn, can be written exactly in terms of the solutions of non-linear
differential equations of the Painlev\'e V type. Equipped with the previous
results, we find the leading terms for the entanglement entropy, both for short
and long distances, and showing that in the intermediate regime it can be
expanded in a series of multiple integrals. The previous results have been
checked by direct numerical calculations on the lattice, finding perfect
agreement. Finally, we comment on a possible generalization of the entanglement
entropy c-theorem to the alpha-entropies.Comment: Clarification in section 2, one reference added. 15 pages, 3 figure
Evolution of entanglement entropy in one-dimensional systems
We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length l and its complement, starting from a pure state which is not an eigenstate of the Hamiltonian. We use path integral methods of quantum field theory as well as explicit computations for the transverse Ising spin chain. In both cases, there is a maximum speed v of propagation of signals. In general the entanglement entropy increases linearly with time t up to t = l/2v, after which it saturates at a value proportional to l, the coefficient depending on the initial state. This behaviour may be understood as a consequence of causality