Theoretical and Mathematical Physics

, Volume 164, Issue 3, pp 1136–1139 | Cite as

Generalized entropy of the Heisenberg spin chain

  • A. R. Its
  • V. E. Korepin


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 


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© 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

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