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Results in Physics

Renormalization of net steered coherence and average coherence in the XXZ model with Dzyaloshinskii–Moriya interaction

Yu-Xia Xie, Yuhang Sun

Published Mar 1, 2024• 2 citations
Publisher

Abstract

The critical behaviors of the net steered coherence (NSC) and average coherence (AC) in the XXZ model with Dzyaloshinsky-Moriya interaction are investigated by adopting the quantum renormalization group method. It is found that they both develop different saturated values in different phases of the model after enough iterations of the renormalization of the coupling constants. In addition, their susceptibilities at the phase transition point are divergent in the thermodynamic limit, and the scaling exponent is determined by the exponent governing the divergence of the correlation length close to the phase transition point. This exemplifies that both the NSC and AC can serve as reliable indicators of quantum phase transitions.

DOI
10.1016/j.rinp.2024.107547

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The critical behaviors of the net steered coherence (NSC) and average coherence (AC) in the XXZ model with Dzyaloshinsky-Moriya interaction are investigated by adopting the quantum renormalization group method. It is found that they both develop different saturated values in different phases of the model after enough iterations of the renormalization of the coupling constants. In addition, their susceptibilities at the phase transition point are divergent in the thermodynamic limit, and the scaling exponent is determined by the exponent governing the divergence of the correlation length close to the phase transition point. This exemplifies that both the NSC and AC can serve as reliable indicators of quantum phase transitions.
Abstract The performance of average coherence (AC) and average correlated coherence (ACC) in detecting quantum phase transitions (QPTs) has been explored by considering the XY model with staggered Dzyaloshinskii-Moriya interaction. By using the quantum renormalization group method, it is shown that the ground-state AC and ACC show either a maximum or a minimum at the QPT point. Moreover, the AC and ACC susceptibilities (i.e. their derivatives with respect to the driving parameter) have two extreme points near the two sides of the QPT point. A finite-scaling analysis reveals that these extreme points tend to the QPT point after several iterations of the renormalization and the susceptibilities at the QPT point become divergent in the thermodynamic limit.
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We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-1/21/21/2 XYXYXY model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.
Abstract With the aid of the quantum renormalization group (QRG) method, we study the multipartite entanglement and quantum phase transitions (QPTs) in the XXZ model with Dzyaloshinskii–Moriya (DM) interaction. The measures employed here are genuine multipartite entanglement (GME-concurrence) and global entanglement. The results show that both multipartite entanglement measures can accurately detect QPTs at the critical points after sufficient iteration steps. By the difference analysis, moreover, we derive an inequality such that the global entanglement is exactly an upper bound of the square GME-concurrence. Actually, this inequality is established whether or not the QRG method is carried out, which discloses some intrinsic features of long-scale multipartite entanglement. Based on the first derivative of GME-concurrence, the non-analytic phenomenon and scaling behaviors with different theoretical exponents are analyzed in detail, showing that the ground states of the XXZ model with DM interaction are asymmetrical.
The critical behaviors of the steered quantum coherence (SQC) in the transverse field XY model with Dzyaloshinsky–Moriya (DM) interaction are explored. It is found that there is an inflexion for the SQC at the critical field of quantum phase transition (QPT) for two long‐distance spins, and there is a divergence for the derivative of the SQC with respect to the magnetic field at the critical field of QPT for any two spins in the chain. Moreover, SQC shows distinct behaviors in different phase regions of the model, which is also a signature of the QPT. Furthermore, the SQC method is robust in studying quantum criticality even under environmental coupling.
Abstract The critical behaviors of average coherence (AC) in a two-dimensional XY model are investigated by using the renormalization group method. It is found that there is an extremum for the AC of the renormalized blocks at the critical point of quantum phase transition (QPT), and a finite-scaling analysis shows that in the thermodynamic limit, there is a divergence for the AC susceptibility at the QPT point. Furthermore, by considering the bipartite division of the renormalized blocks, it is found that the AC is monogamous and the average correlated coherence is polygamous, and the corresponding monogamy score is also a reliable indicator of QPT. Some constraints on the shareability of AC among the renormalized blocks are also obtained.