One-norm geometric quantum discord of two-qubit state in spin chain environment at finite temperature

•One-norm GQD is more robust than QD against the decoherence at finite temperature.•One-norm GQD is superior to QD in detecting the critical point of QPT of the spin chain.•The phenomena of sudden transition and double sudden transitions are analyzed.•The methods to control the frozen time of quantum correlations are proposed.

We study the dynamics of quantum correlations measured by quantum discord (QD) and one-norm geometric quantum discord (GQD) in a two-qubit system coupled to an XY spin chain with finite temperature. It is shown that one-norm GQD is more robust than QD against the decoherence induced by the spin chain with finite temperature, and one-norm GQD is superior to QD in detecting the critical point of quantum phase transition (QPT) of the spin chain. Considering the effects of the state parameters, the temperature of the spin chain and the asymmetric coupling parameter, we analyze the phenomenons of sudden transition and double sudden transitions occurred in the evolutions of QD and one-norm GQD. Besides, the influences of the Dzyaloshinsky–Moriya (DM) interaction and the three-site interaction in the spin chain are also taken into account.