Theoretical and Mathematical Physics

, Volume 164, Issue 3, pp 1136-1139

First online:

Generalized entropy of the Heisenberg spin chain

  • A. R. ItsAffiliated withDepartment of Mathematical Sciences, Indiana University-Purdue University Indianapolis Email author 
  • , V. E. KorepinAffiliated withYang Institute for Theoretical Physics, State University of New York

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


We consider the XY quantum spin chain in a transverse magnetic field. We consider the Rényi entropy of a block of neighboring spins at zero temperature on an infinite lattice. The Rényi entropy is essentially the trace of some power α of the density matrix of the block. We calculate the entropy of the large block in terms of Klein’s elliptic λ-function. We study the limit entropy as a function of its parameter α. We show that the Rényi entropy is essentially an automorphic function with respect to a certain subgroup of the modular group. Using this, we derive the transformation properties of the Rényi entropy under the map α → α −1 .


quantum entanglement spin chain Bethe ansatz