A quantum correlation test of quantum criticality in transverse-field Ising chain with Dzyaloshinskii-Moriya interaction

Usually, the zero temperature quantum critical point (QCP) induces a QC regime at low temperature due to the competition between quantum and thermal fluctuations, which is characterized by power-law temperature dependence of thermodynamics. Herein, focusing on the quantum phase transition (QPT) of transeverse-field Ising chain with Dzyaloshinskii-Moriya (DM) interaction, the quantum correlation exhibits temperature scaling. In the absence of magnetic field, the competition between DM interaction and Ising spin coupling manifested by θ angle, gives rise to different ground states such as Ising-type ferromagnetic (xFM), antiferromagnetic (xAFM) and Tomonaga-Luttinger liquid (TLL). As temperature emerges, the TLL phase is crossover into QC regimes with a crossover temperature connecting to a universal linear line T*~|θ-θ_c1,2| that ends at θ_c1,2 upon cooling down to 0 K, providing a new clue to capture QCP. Around QCP, the thermal QC scaling is demonstrated by analyzing quantum correlations and specific heat to extract the critical exponents (δ, β, γ and α) that fulfill the Widom and Essam-Fisher scaling laws, which is further verified by scaling hypothesis equations. As a magnetic field is turned on, an additional field-induced transverse ferromagnetic (zFM) phase with gapped low-lying excitation is unveiled. In particular, the Ising-like quantum criticality turns out to be gapless, which is different from the TLL-like one.