Theoretical and Mathematical Physics

, Volume 198, Issue 2, pp 296–315 | Cite as

Exact Results for the Isotropic Spin-1/2 Heisenberg Chain With Dissipative Boundary Driving

  • V. Yu. PopkovEmail author
  • D. Karevski
  • G. M. Schütz


We consider the open isotropic spin-1/2 Heisenberg quantum spin chain with a finite number N of sites coupled at the ends to a dissipative environment that favors polarization of the boundary spins in different directions. We review the matrix product ansatz (MPA) that yields the exact reduced density matrix of the Heisenberg chain. We develop the matrix algebra coming from the MPA in more detail than in previous work. We hence obtain exact results for the nonequilibrium partition function, about the impact of quantum fluctuations on the targeted boundary states, and for current–magnetization correlations in the steady state. The boundary states turn out to be pure to the order o(N−2). We show that the local magnetization and the local current perpendicular to the plane spanned by the boundary polarizations exhibit long-range correlations while the local magnetization correlations with the local in-plane currents are strongly suppressed.


nonequilibrium steady state Heisenberg spin chain driven system exact result 


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Helmholtz Institute for Radiation and Nuclear PhysicsUniversity of BonnBonnGermany
  2. 2.Institute of Theoretical PhysicsUniversity of CologneCologneGermany
  3. 3.Laboratoire de Physique et Chimie Théoriques, Université de Lorraine, CNRSVandoeuvre les Nancy CedexLondonFrance
  4. 4.Institute of Complex Systems IIForschungszentrum JülichJülichGermany

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