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We show that the nearest neighbour entanglement in a mixture of ground andfirst excited states - a subjacent state - of the J1-J2 Heisenberg quantum spinchain can be used as an order parameter to detect the phase transition of thechain from a gapless spin fluid to a gapped dimer phase. We study theeffectiveness of the order parameter for varying relative mixing probabilitiesbetween the ground and first excited states in the subjacent state fordifferent system sizes, and extrapolate the results to the thermodynamic limit.We observe that the nearest neighbour concurrence can play a role of a goodorder parameter even if the system is in the ground state, but with a smallfinite probability of leaking into the first excited state. Moreover, we applythe order parameter of the subjacent state to investigate the response toseparate introductions of anisotropy and of glassy disorder on the phasediagram of the model, and analyse the corresponding finite-size scale exponentsand the emergent tricritical point in the former case. The anisotropic J1-J2chain has a richer phase diagram which is also clearly visible by using thesame order parameter.

Estimating phase transition of perturbed J1-J2 Heisenberg quantum chain in mixtures of ground and first excited states