Theoretical and Mathematical Physics

, Volume 164, Issue 3, pp 1136–1139

Generalized entropy of the Heisenberg spin chain


DOI: 10.1007/s11232-010-0091-6

Cite this article as:
Its, A.R. & Korepin, V.E. Theor Math Phys (2010) 164: 1136. doi:10.1007/s11232-010-0091-6


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 entanglementspin chainBethe ansatz

Copyright information

© MAIK/Nauka 2010

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIndiana University-Purdue University IndianapolisIndianapolisUSA
  2. 2.Yang Institute for Theoretical PhysicsState University of New YorkStony BrookUSA