Renyi Entropy of the XY Spin Chain

Understand

We consider the one-dimensional XY quantum spin chain in a transverse magnetic field.

• We are interested in the Renyi entropy of a block of L neighboring spins at zero temperature on an infinite lattice.
• The Renyi entropy is essentially the trace of some power $\alpha$ of the density matrix of the block.
• We calculate the asymptotic for $L \to \infty$ analytically in terms of Klein's elliptic $\lambda$ - function.