Entanglement and quantum phase transition in a mixed-spin Heisenberg chain with single-ion anisotropy

2011 ◽  
Vol 390 (11) ◽  
pp. 2208-2214 ◽  
Author(s):  
E. Solano-Carrillo ◽  
R. Franco ◽  
J. Silva-Valencia
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transition ◽  
Quantum Phase ◽  
Heisenberg Chain ◽  
Mixed Spin

scholarly journals Quantum discord and quantum phase transition in spin-1/2 frustrated Heisenberg chain

2013 ◽  
Vol 13 (5&6) ◽  
pp. 452-468
Author(s):  
Chu-Hui Fan ◽  
Heng-Na Xiong ◽  
Yixiao Huang ◽  
Zhe Sun
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transition ◽  
Quantum Discord ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Quantum Phase ◽  
Nonlinear Dependence ◽  
Heisenberg Chain ◽  
Transition Points ◽  
Analytical Result

By using the concept of the quantum discord (QD), we study the spin-1/2 antiferromagnetic Heisenberg chain with next-nearest-neighbor interaction. Due to the $SU(2)$ symmetry and $Z_{2}$ symmetry in this system, we obtain the analytical result of the QD and its geometric measure (GMQD), which is determined by the two-site correlators. For the 4-site and 6-site cases, the connection between GMQD (QD) and the eigenenergies was revealed. From the analytical and numerical results, we find GMQD (QD) is an effective tool in detecting the both the first-order and the infinite-order quantum-phase-transition points for the finite-size systems. Moreover, by using the entanglement excitation energy and a universal frustration measure we consider the frustration properties of the system and find a nonlinear dependence of the GMQD on the frustration.

scholarly journals Reply to “Comment on ‘Quantum phase transition in the four-spin exchange antiferromagnet’ ”

2010 ◽  
Vol 82 (13) ◽  
Author(s):  
Valeri N. Kotov ◽  
D. X. Yao ◽  
A. H. Castro Neto ◽  
D. K. Campbell
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transition ◽  
Spin Exchange ◽  
Quantum Phase
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