Total quantum coherence close to the quantum critical points in the XXZ model with Dzyaloshinskii–Moriya interaction

Abstract

In this paper, by using the quantum renormalization-group method, we study the relation between total quantum coherence based on norm and quantum phase transition in the XXZ model with Dzyaloshinskii–Moriya (DM) interaction. Our findings reveal a distribution relation of quantum coherence in this model, i.e. the value of the quantum coherence of a three-site block state is equal to the sum of its reduced state coherence, and this characteristic can be generalized to a multipartite system. Meanwhile, because of favoring the alignment of spins, the anisotropy suppresses the quantum coherence; on the other hand, by creating the quantum fluctuations, the DM interaction can effectively enhance the value of quantum coherence. Additionally, after several iterations of the renormalization, quantum coherence of the whole block state can form two saturated values, which are related to two different phases: spin-fluid phase and Néel phase. Furthermore, we discover that the total quantum coherence of the block–block state obeys the nonanalytic and scaling properties with the quantum coherence exponent associated with correlation length.