Steered Quantum Coherence and Quantum Criticality in the XY Model with Dzyaloshinsky–Moriya Interaction

Abstract

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.

Steered Quantum Coherence as a Signature of Topological Quantum Phase Transitions in the Extended XY Model

“…[9][10][11][12][13][14][15][16][17][18][19][20][21][22] One of them is the SQC. [18,20,23] The SQC characterizes a hybrid of the two notions of correlations and coherence. In 2020, Hu et al [18] first proposed to detect QPTs by using SQC and DOI: 10.1002/andp.202300121 analyzed its especial advantages in characterizing QPTs.…”

“…[18] The SQC has recently been developed to study the QPTs of the Lipkin-Meshkov-Glick model and the transverse field XY model with Dzyaloshinsky-Moriya (DM) interaction. [20,23] The above study only focus on the conventional QPTs. Inspired by them, we wonder whether the SQC or its first-order derivative can succeed in signaling the critical points of TQPTs.…”

Correlation-induced coherence and its use in detecting quantum phase transitions

“…More examples involving other coherence measures, such as the total quantum coherence, the local and intrinsic quantum coherence, and the coherence measure based on the Jensen-Shannon divergence, can be found in Refs. [57,[59][60][61][62][63][64][65][66].…”

Finite-size scaling of coherence and steered coherence in the Lipkin-Meshkov-Glick model

“…One of these coherence-based quantifiers is the steered coherence for a bipartite state ρ AB , including the average steered coherence (ASC) with respect to the mutually unbiased bases [24][25][26] and the maximal steered coherence (MSC) in the eigenbasis of ρ B = tr A ρ AB [28]. The feasibility of the ASC in signaling QPTs has been validated for certain spin systems [29,30], and compared with entanglement and quantum discord, it has the benefit of being long ranged, thus releases the strict restriction on the choice of special spins for probing QPTs.…”