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Physica Scripta

Spin nonclassicality and quantum phase transition in the XY spin model

Hao Dai, Shuangshuang Fu, Shunlong Luo

Published Sep 16, 2020• 5 citations
Publisher

Abstract

Abstract We study the behaviors of spin nonclassicality in critical systems of spin chains, with the spin nonclassicality measured by an informational quantifier based on the Wigner-Yanase skew information. For the XY spin chain with three-spin interaction, we evaluate both the single-spin and the nearest neighbour two-spin nonclassicalities, as well as their first-order derivatives. We demonstrate the effectiveness of these quantities of spin nonclassicality in revealing the critical points for quantum phase transition. The merits of the present approach to detecting quantum phase transition by spin nonclassicality lie in its easy computation, informational content and metrological significance.

DOI
10.1088/1402-4896/abb910

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Abstract We study the behaviors of spin nonclassicality in critical systems of spin chains, with the spin nonclassicality measured by an informational quantifier based on the Wigner-Yanase skew information. For the XY spin chain with three-spin interaction, we evaluate both the single-spin and the nearest neighbour two-spin nonclassicalities, as well as their first-order derivatives. We demonstrate the effectiveness of these quantities of spin nonclassicality in revealing the critical points for quantum phase transition. The merits of the present approach to detecting quantum phase transition by spin nonclassicality lie in its easy computation, informational content and metrological significance.
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We investigate the behaviors of Wigner–Yanase skew information and the l1 norm, as two different measures of quantum coherence, in a tripartite ground state of the anisotropic spin-1/2 XY model. Following the renormalization-group method, we analytically link the two measures with each other and with the ground state energy of the system. We demonstrate that both the quantities show distinctive behaviors at the critical point of the system. The analysis of the first derivatives of the quantities reveals nonanalyticity in their behaviors, capturing quantum phase transition. The scaling behavior of the system is analyzed and it is shown that the minimum of the first derivative of Wigner–Yanase skew information converges to zero and the maximum of the first derivative of l1 norm diverges and both approach to the critical point with increasing size of the system.
We explore the local quantum coherence and the local quantum uncertainty, based on Wigner-Yanase skew information, in the ground state of the anisotropic spin-1/2 XY chain in a transverse magnetic field. We show that the skew information, as a figure of merit, supplies the necessary information to reveal the occurrence of the second-order phase transition and the completely factorized ground state in the XY model. Additionally, in the same context, we also discuss the usefulness of a simple experimentally friendly lower bound of local quantum coherence. Furthermore, we demonstrate how the connection between the appearance of nonanalyticities in the local quantum uncertainty of the ground state and the quantum phase transitions does not hold in general, by providing explicit examples of the situation. Lastly, we discuss the ability of the local quantum coherence to accurately estimate the critical point of the phase transition, and we investigate the robustness of the factorization phenomenon at low temperatures.
Quantum phase transition in the XYXYXY spin model with three-spin interaction is investigated using magic resource (non-stabilizerness), which is crucial in universal fault-tolerant quantum computation. The magic quantifier we employ here is defined straightforwardly via characteristic functions of quantum states, which are well defined for all dimensional quantum systems (in sharp contrast to those defined by discrete Wigner functions) and can be easily calculated. We show that the magic quantifier of both the reduced single-site spins and two-site spins of the system ground state increase to their maximum around the critical points for quantum phase transition. This indicates that the magic resource can be used to detect the critical phenomena in the XYXYXY spin model and reveals a connection between quantum phase transition in many-body systems and quantum resource in stabilizer quantum computation.
\n\nWe apply the Wigner-Yanase skew information approach to analyze two typical models that exhibit a topological quantum phase transition. Based on the exact solutions of the ground states, the Wigner-Yanase skew information between two nearest sites for each of the two models is obtained. For the one-dimensional Kitaev chain model, the first-order derivative of the Wigner-Yanase skew information is non-analytical around the critical point. The scaling behavior and the universality are verified numerically. In particular, the skew information can also detect the factorization transition in such a model. For the two-dimensional Kitaev honeycomb model, the first-order derivative of the Wigner-Yanase skew information shows some singularities at the critical points where the system transits from the gapless phase to the gapped one. Our results suggest that the Wigner-Yanase skew information can serve as a good indicator of the topological phase transitions in these models and shed considerable light on the relationships between topological quantum phase transition and information theory.\n
Abstract In this article we consider two spin-1/2 chains described, respectively, by the thermodynamic limit of the XY model with the usual two site interaction, and an extension of this model (without taking the thermodynamics limit), called XYT , were a three site interaction term is presented. To investigate the critical behaviour of such systems we employ tools from quantum information theory. Specifically, we show that the local quantum uncertainty, a quantity introduced in order to quantify the minimum quantum share of the variance of a local measurement, can be used to indicate quantum phase transitions presented by these models at zero temperature. Due to the connection of this quantity with the quantum Fisher information, the results presented here may be relevant for quantum metrology and quantum thermodynamics.