Eur. Phys. J. Plus (2017) 132: 215
https://doi.org/10.1140/epjp/i2017-11492-x

Regular Article

Analytic renormalized bipartite and tripartite quantum discords with quantum phase transition in XXZ spins chain

¹ Department of Physics, Quaid-i-Azam University, Islamabad, Pakistan
² Department of Physics, COMSATS Institute of Information Technology, Park Road, 45550, Islamabad, Pakistan
³ NIMS, Tsukuba, 305-0044, Ibaraki, Japan
⁴ Center of High Energy Physics, University of Punjab, Pakistan, Japan-Pakistan Collaboration, 448-18, Ozone, Japan

^* e-mail: sksafi@comsats.edu.pk

Received: 21 December 2016
Accepted: 10 April 2017
Published online: 15 May 2017

Abstract

The behavior of bipartite quantum discord (BQD) and tripartite quantum discord (TQD) in the Heisenberg XXZ spins chain is investigated with the increasing size of the system using the approach of the quantum renormalization group method. Analytical relations for both BQD and TQD are obtained and the results are checked through numerical optimization. In the thermodynamics limit, both types of discord exhibit quantum phase transition (QPT). The boundary of QPT links the phases of saturated discord and zero discord. The first derivative of both discords becomes discontinuous at the critical point, which corresponds to the second-order phase transition. Qualitatively identical, the amount of saturated BQD strongly depends on the relative positions of spins inside a block. TQD can be a better candidate than BQD both for analyzing QPT and implementing quantum information tasks. The scaling behavior in the vicinity of the critical point is discussed.