Renormalization of concurrence: the application of quantum renormalization group to the quantum information systems

Abstract

We have combined the idea of renormalization group and quantum information theory. We have shown how the entanglement or concurrence evolve as the size of the system being large, i.e. the finite size scaling is obtained. Moreover, It introduces how the renormalization group approach can be implemented to obtain the quantum information properties of a many body system. We have obtained the concurrence as a measure of entanglement, its derivatives and their scaling behavior versus the size of system for the one dimensional Ising model in transverse field. We have found that the derivative of concurrence between two blocks each containing half of the system size diverges at the critical point with the exponent which is directly associated with the divergence of the correlation length.

4 pages, 5 eps figures

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• 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
• Performance of various correlation measures in quantum renormalization-group method: A case study of quantum phase transition
• Induced effects of the Dzyaloshinskii-Moriya interaction on the thermal entanglement in spin-1/2 Heisenberg chains
• Ground-state fidelity of the spin-1 Heisenberg chain with single ion anisotropy: quantum renormalization group and exact diagonalization approaches
• Quantum renormalization group of XY model in two dimensions
• Quantum Renormalization Group for Ground-State Fidelity
• Thermal entanglement between non-nearest-neighbor spins on fractal lattices
• Quantum renormalization group approach to geometric phases in spin chains
• The phase diagram of the extended anisotropic ferromagnetic-antiferromagnetic Heisenberg chain
• Topological phase transiton of anisotropic XY model with Dzyaloshinskii-Moriya interaction
• Distribution of quantum coherence and quantum phase transition in the Ising system
• 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
• Quantum critical phase diagram of bond alternating Ising model with Dzyaloshinskii-Moriya interaction: signature of ground state fidelity
• Universal quantum correlation close to quantum critical phenomena
• Spotlighting quantum phase transition in spin-1/2 Ising-Heisenberg diamond chain employing Measurement-Induced Nonlocality
• Genuine tripartite entanglement as a probe of quantum phase transitions in a spin-1 Heisenberg chain with single-ion anisotropy
• Quantum Quench dynamics in XY spin chain with ferromagnetic and antiferromagnetic interactions
• Quantum phase transitions in the Kondo-necklace model: Perturbative continuous unitary transformation approach
• Entanglement and Quantum Phase Transitions via Adiabatic Quantum Computation
• Scaling of quantum correlation and monogamy relation near a quantum phase transitions in two-dimensional XY spin system