Elisa Ercolessi, Stefano Evangelisti, Fabio Franchini, Francesco Ravanini
We study analytically the corrections to the leading terms in the Renyi
entropy of a massive lattice theory, showing significant deviations from naive
expectations. In particular, we show that finite size and finite mass effects
give rise to different contributions (with different exponents) and thus
violate a simple scaling argument.
In the specific, we look at the entanglement entropy of a bipartite XYZ
spin-1/2 chain in its ground state. When the system is divided into two
semi-infinite half-chains, we have an analytical expression of the Renyi
entropy as a function of a single mass parameter. In the scaling limit, we show
that the entropy as a function of the correlation length formally coincides
with that of a bulk Ising model. This should be compared with the fact that, at
criticality, the model is described by a c=1 Conformal Field Theory and the
corrections to the entropy due to finite size effects show exponents depending
on the compactification radius of the theory. We will argue that there is no
contradiction between these statements.
If the lattice spacing is retained finite, the relation between the mass
parameter and the correlation length generates new subleading terms in the
entropy, whose form is path-dependent in phase-space and whose interpretation
within a field theory is not available yet. These contributions arise as a
consequence of the existence of stable bound states and are thus a distinctive
feature of truly interacting theories, such as the XYZ chain.
View original:
http://arxiv.org/abs/1201.6367
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