Quantum correlations in a cluster spin model with three-spin interactions

Abstract An exactly solvable cluster spin model with three-spin interaction couplings J x (for XZX spin components) and J y (for YZY spin components) in the presence of a transverse magnetic field h for a spin chain is investigated. For h = 0, and with only one non-zero interaction strength, the ground state is the cluster state. Through the Jordan–Wigner fermion mapping, the odd sites and the even sites form two separate transverse- XY chains, connected only through the boundary terms. Consequently, all measures of quantum correlations for nearest neighbour spins, the concurrence, the quantum mutual information and the quantum discord are all zero in the ground state. The dynamics is spin conserving for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mi>y</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>J</mml:mi> <mml:mi>x</mml:mi> </mml:msub> </mml:mrow> </mml:math> , exhibiting a line of critical points for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> <mml:mi>h</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mi>x</mml:mi> </mml:msub> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mtext>⩽</mml:mtext> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , with an uncorrelated direct product ground state for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> <mml:mi>h</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mi>x</mml:mi> </mml:msub> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mo>&gt;</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> . There are several quantum critical points in the parameter space, with multi-fold degenerate ground states. The magnetisation and the global entanglement measure exhibit strong singular features for the spin conserving case. The next-neighbour quantum correlation measures are investigated analytically, which exhibit singular features in the vicinity of degeneracy critical points. The J y - and h - derivatives of the concurrence exhibit singular peak behaviour near the degeneracy critical points, except in the spin conserving case where the derivatives are zero.