ABSTRACT The ground‐state phase transition for the spin‐1/2 Heisenberg chain with ‐direction dimerized anisotropy is investigated by exploiting the infinite time‐evolving block decimation algorithm. Phase boundaries are identified by examining the von Neumann entropy, entanglement spectrum, and several of fidelity indicators. The phase diagram features the existence of a tri‐critical point, which signifies the complete convergence of the transition boundaries separating the Odd‐Haldane, Even‐Haldane, and Néel phases. Specifically, the high‐precision fit of the Tomonaga–Luttinger liquid parameter provides evidence for a Tomonaga–Luttinger liquid phase line which splits the Odd‐Haldane and Even‐Haldane phases. Along this critical line, it is found that the critical exponent exhibits a variation with the bond dimerization strength, which is according to a power‐law scaling. This provides a crucial theoretical framework for analyzing critical behaviors associated with topological phase transitions in quantum many‐body systems. From the odd and even string order parameters and the non‐local Néel order parameter, the Haldane phases and the Néel phase are characterized. Furthermore, the central charge and critical exponent are identified by performing a scaling analysis of finite correlation length and order parameters, indicating that the phase transition between the Haldane phases and Néel phase belongs to the classical Ising universality class, as well as a Gaussian phase transition between two types of Haldane phases.
Jin et al. (Sun,) studied this question.