Entanglement entropy in fermionic chains.

F. Ares, J.V. Esteve, F. Falceto

Departamento de Física Teórica. Fac. De Ciencias. U. Zaragoza

Instituto de biocomputación y física de sistemas complejos. U. Zaragoza.

We present a few results on the Renyi entanglement entropy for stationary states in a homogeneous, quantum, fermionic chain. We first discuss the case of an interval, where analytical tools for the computation are available. We find that, for certain states, one

obtains a volume law and possible logarithmic subdominant corrections. By introducing non local interactions in the chain, we can consider the previous as the ground states of fermionic ladders, which leads to a natural physical interpretation for the scaling properties of the entanglement entropy and its universality. Then we move on to the case of several intervals and present a new expression for the asymptotic behaviour of the entanglement entropy. We support our result with clear numerical evidences. This leads to a mathematical conjecture on the asymptotic behaviour of principal submatrices of a Toeplitz matrix.