Thermodynamics and correlations featured quantum criticality of transverse-field Ising model with off-diagonal exchange interactions

Abstract

We study the quantum phase transitions (QPTs) and quantum criticality of transverse-field Ising model with off-diagonal exchange interactions. In the absence of magnetic field, the clockwise spiral (CWS), counterclockwise spiral (CCWS) and longitudinal ferromagnetic (xFM) phases are revealed by the spin chirality vector κz and longitudinal spin–spin correlation Cxx mutually. The general QPT is diagnosed by the temperature power-law divergence of Grüneisen ratio (GR) Γ∼±T−1. The critical scaling is further done to capture the quantum critical point (QCP) by analyzing κz and specific heat, which offers a direct access to distill the critical exponents (δ, β, α) that fulfill the Essam–Fisher relation α+β(1+δ)=2, providing a new clue to detect the general QPT. Subsequently, some scaling hypothesis equations are proposed to check the scaling analysis. In a magnetic field, an additional field-induced transverse ferromagnetic (zFM) phase is unveiled. Specifically, for the xFM phase transition into zFM one, the transverse-field Ising terms predominates, which approximately keeps the Z2 symmetry at hc=1, giving rise to the self-dual quantum criticality, demonstrated by the constant of GR irrelevant of temperature. Furthermore, the gapped and gapless low-lying excitations of quantum phases are manifested by the thermal Drude weight and specific heat.