Performance of various correlation measures in quantum renormalization-group method: A case study of quantum phase transition

Abstract

We have investigated quantum phase transition employing the quantum renormalization group (QRG) method while in most previous literature barely entanglement (concurrence) has been demonstrated. However, it is now well known that entanglement is not the only signature of quantum correlations and a variety of computable measures have been developed to characterize quantum correlations in the composite systems. As an illustration, two cases are elaborated: one dimensional anisotropic (i) XXZ model and (ii) XY model, with various measures of quantum correlations, including quantum discord (QD), geometric discord (GD), measure-induced disturbance (MID), measure-induced nonlocality (MIN) and violation of Bell inequalities (eg. CHSH inequality). We have proved that all these correlation measures can effectively detect the quantum critical points associated with quantum phase transitions (QPT) after several iterations of the renormalization in both cases. Nonetheless, it is shown that some of their dynamical behaviors are not totally similar with entanglement and even when concurrence vanishes there still exists some kind of quantum correlations which is not captured by entanglement. Intriguingly, CHSH inequality can never be violated in the whole iteration procedure, which indicates block-block entanglement can not revealed by the CHSH inequality. Moreover, the nonanalytic and scaling behaviors of Bell violation have also been discussed in detail. As a byproduct, we verify that measure-induced disturbance is exactly equal to the quantum discord measured by σ_z for general X-structured states.

Published version. 10 pages, 8 figures

References in corpus (33)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Introducing Quantum Discord
• Entanglement in quantum critical phenomena
• Classical, quantum and total correlations
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• Necessary and sufficient condition for non-zero quantum discord
• Quantum discord for two-qubit X-states
• Classical Correlation and Quantum Discord in Critical Systems
• Quantum Phase Transitions and Bipartite Entanglement
• Non-Markovian Dynamics of Quantum Discord
• Quantum correlations in spin chains at finite temperatures and quantum phase transitions
• Quantum discord and quantum phase transition in spin chains
• Quantum discord of two-qubit X-states
• System-reservoir dynamics of quantum and classical correlations
• Entanglement, quantum phase transition and scaling in XXZ chain
• Optimal measurements to access classical correlations of two-qubit states
• Phase Diagram and Entanglement of Ising Model With Dzyaloshinskii-Moriya Interaction
• Dzyaloshinskii-Moriya Interaction and Anisotropy effects on the Entanglement of Heisenberg Model
• Correlations in local measurements on a quantum state, and complementarity as an explanation of nonclassicality
• The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model
• The ground state entanglement in the $XXZ$ model
• Renormalization of concurrence: the application of quantum renormalization group to the quantum information systems
• Entanglement and quantum phase transition in the one-dimensional anisotropic XY model
• Quantum entanglement and quantum phase transition in the XY model with staggered Dzyaloshinskii-Moriya interaction
• Quantum renormalization group of XYZ model in a transverse magnetic field
• Bell inequalities and entanglement at quantum phase transition in the XXZ Model
• Nonlocality and entanglement in the XY model
• Analytic Formulations of the Density Matrix Renormalization Group
• Phase Diagram of the One Dimensional $S=1/2$ $XXZ$ model with Ferromagnetic nearest-neighbor and Antiferromagnetic next-nearest neighbor interactions
• Phase diagram of the anti-ferromagnetic xxz model in the presence of an external magnetic field
• Second order quantum renormalisation group of XXZ chain with next nearest neighbour interactions
• Real Space Renormalization Group Methods and Quantum Groups

Cited by in corpus (14)

• Quantum discord and its allies: a review
• Scaling of genuine multiparticle entanglement at a quantum phase transition
• Exact dynamics of quantum correlations of two qubits coupled to bosonic baths
• Quantum versus mean-field collapse in a many-body system
• Novel Approach to Unveil Quantum Phase Transitions Using Fidelity Map
• Suppression of the quantum collapse in binary bosonic gases
• Thermal quantum coherence of two-qutrit Heisenberg XXZ model with Herring-Flicker coupling and Dzyaloshinskii-Moriya interaction under magnetic field
• Renormalization of trace distance and multipartite entanglement close to the quantum phase transitions of one- and two-dimensional spin-chain systems
• Multipartite entanglement, quantum coherence, and quantum criticality in triangular and Sierpiński fractal lattices
• Universal quantum correlation close to quantum critical phenomena
• The intrinsic relations of quantum resources in multiparticle systems
• Spotlighting quantum phase transition in spin-1/2 Ising-Heisenberg diamond chain employing Measurement-Induced Nonlocality
• Cumulative measure of correlation for multipartite quantum states
• Scaling of quantum correlation and monogamy relation near a quantum phase transitions in two-dimensional XY spin system