Exploring the Koch fractal lattice with quantum renormalization group method

Abstract

We investigate quantum criticality of many-body systems in the context of dimensions through the behavior of tripartite entanglement and tripartite quantum coherence. Following the approach of quantum renormalization group (QRG) method, the analysis on one-dimensional Heisenberg Ising model and non-integer Hausdorff dimensional Koch fractal lattice is made with the increasing size of the systems and anisotropy in the spin components. In thermodynamics limit, the two quantities develop three different regions for each system, signaling the existence of two critical points. The presence of quantum criticality is supported by the divergence of the first derivative of both quantities and their scaling with the increasing number of particles. Our study shows that quantum criticality in the non-integer Hausdorff dimension of Koch fractal lattice is more sensitive to the size than in the one-dimensional spin chains.