Multipartite entanglement, quantum coherence, and quantum criticality in triangular and Sierpiński fractal lattices

Abstract

We investigate the quantum phase transitions of the transverse-field quantum Ising model on the triangular lattice and Sierpiński fractal lattices by employing multipartite entanglement and quantum coherence along with the quantum renormalization group method. It is shown that the quantum criticalities of these high-dimensional models closely relate to the behaviors of the multipartite entanglement and quantum coherence. As the thermodynamic limit is approached, the first derivatives of multipartite entanglement and quantum coherence exhibit singular behaviors and the consistent finite-size scaling behaviors for each lattice are also obtained from the first derivatives. The multipartite entanglement and quantum coherence are demonstrated to be good indicators for detecting the quantum phase transitions in the triangular lattice and Sierpiński fractal lattices. Furthermore, the factors that determine the relations between the critical exponents and the correlation length exponents for these models are diverse. For the triangular lattice, the decisive factor is the spatial dimension, while for the Sierpiński fractal lattices, it is the Hausdorff dimension.

12 pages; 12 figures

References in corpus (15)

• Quantum Phase Transitions and Bipartite Entanglement
• The Fidelity and Trace Norm Distances for Quantifying Coherence
• Properties of Classical and Quantum Jensen-Shannon Divergence
• Entanglement and Quantum Phase Transition Revisited
• On the metric character of the quantum Jensen-Shannon divergence
• Monogamy of quantum correlations - a review
• The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model
• Performance of various correlation measures in quantum renormalization-group method: A case study of quantum phase transition
• Phase Diagram of the One Dimensional $S=1/2$ $XXZ$ model with Ferromagnetic nearest-neighbor and Antiferromagnetic next-nearest neighbor interactions
• Quantum coherence of planar spin models with Dzyaloshinsky-Moriya interaction
• Multi-partite entanglement and quantum phase transition in the one-, two-, and three-dimensional transverse field Ising model
• Quantum renormalization group of XY model in two dimensions
• Real-space renormalization group for the transverse-field Ising model in two and three dimensions
• Spectral density of mixtures of random density matrices for qubits
• Quantum critical behavior of the quantum Ising model on fractal lattices

Cited by in corpus (3)

• Quantum phase transitions and composite excitations of antiferromagnetic spin trimer chains in a magnetic field
• Magnon, doublon and quarton excitations in 2D S=1/2 trimerized Heisenberg models
• Single-ion anisotropy effects on the critical behaviors of quantum entanglement and correlation in the spin-1 Heisenberg chain