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Physica A Statistical Mechanics and its Applications

Renormalization of steered coherence and quantum phase transitions in the alternating Ising model

Yu-Xia Xie, Yuhang Sun

Published Feb 24, 2023• 10 citations
Publisher
DOI
10.1016/j.physa.2023.128617

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Stability of the phase transition and critical behavior of the Ising model against quantum perturbation

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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.
We propose to use the steered quantum coherence (SQC) as a signature of quantum phase transitions (QPTs). By considering various spin chain models, including the transverse-field Ising model, XY\mathit{XY}XY model, and XX\mathit{XX}XX model with three-spin interaction, we showed that the SQC and its first-order derivative succeed in signaling different critical points of QPTs. In particular, the SQC method is effective for any spin pair chosen from the chain, and the strength of SQC, in contrast to entanglement and quantum discord, is insensitive to the distance (provided it is not very short) of the tested spins, which makes it convenient for practical use as there is no need for careful choice of two spins in the chain.
Abstract Symmetric quantum properties and correlations have been often used earlier to study quantum phase transitions in many body systems and spin models. However, the use of asymmetric quantum features, such as steering, have attracted smaller amount of attention in this context, so far. We study EPR steering and quantum phase transitions in the Ising model in transverse field and in the anisotropic XY model by using steering robustness and quantum renormalization group method. The key ingredients of the quantum criticality near the critical points, such as finite-size scaling behaviour and critical exponents, are investigated in detail with two commonly used spin models. Our results show that the first derivative of steering robustness between two blocks diverges near the quantum phase transition points for both models, and exhibits a finite-size scaling effect. Moreover, we explore in detail the asymmetric character of EPR steering, by taking into accounts finite-size effects and measurement number, in the reduced block state in the anisotropic XY model. The results imply that one-way EPR steering does not exist in large system under the limit L → ∞ despite the fact that EPR steering for the reduced block state is asymmetric.