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 lcz and longitudinal spin-spin correlation C-xx mutually. The general QPT is diagnosed by the temperature power-law divergence of Gruneisen ratio (GR) F ~ +/- T-1. The critical scaling is further done to capture the quantum critical point (QCP) by analyzing lcz and specific heat, which offers a direct access to distill the critical exponents (delta, beta, alpha) that fulfill the Essam-Fisher relation alpha + beta(1 + delta)=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 Z(2) symmetry at h(c) = 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. (C) 2022 Elsevier B.V. All rights reserved.
NSTL
Elsevier