Thermal Drude weight signature of gapless quantum criticality: From interacting Kitaev topological superconductor to antiferromagnetic transverse-field Ising chain

Abstract

Within the combination of two-step Jordan-Wigner transformations and one spin rotation, the interacting Kitaev topological superconductor model has been solved exactly, which will be further generalized and transformed into an antiferromagnetic transverse-field Ising chain by the vanishing of electron-electron interaction (U = 0) together with a local unitary transformation in a transverse field. The continuous quantum phase transition is marked by a quantum critical point (QCP), yielding a characteristic quantum critical fan at low temperature owing to the interplay between quantum and thermal fluctuations. It is shown that the plentiful gapped quantum phases and their crossovers are characterized by thermodynamics. In particular, the thermal Drude weight Dth(T = 0) = 0 together with an activated behavior modulated by a power law as T → 0, demonstrate the gapped low-lying excitation. However, at the QCP, Dth(T = 0) > 0 as well as the linear relation dependence on temperature at ultra-low temperature, indicates the gapless quantum criticality, where two distinct gapped quantum phases touch and compete with each other accompanied by the accumulation of entropy.