Entanglement renormalization of anisotropic XY model

Abstract

The renormalization group flows of the one-dimensional anisotropic XY model and quantum Ising model under a transverse field are obtained by different multiscale entanglement renormalization ansatz schemes. It is shown that the optimized disentangler removes the short-range entanglement by rotating the system in the parameter space spanned by the anisotropy and the magnetic field. It is understood from the study that the disentangler reduces the entanglement by mapping the system to another one in the same universality class but with smaller short range entanglement. The phase boundary and corresponding critical exponents are calculated using different schemes with different block sizes, look-ahead steps and truncation dimensions. It is shown that larger truncation dimension leads to more accurate results and that using larger block size or look-ahead step improve the overall calculation consistency.

Quantum impurity in a Luttinger liquid: Universal conductance with entanglement renormalization

“…The MERA is a flexible real space RG scheme based on the tensor network and is designed to retain only the long-range entanglement of the system. 26,27,[37][38][39][40][41] This makes MERA an ideal method for simulating quantum critical systems with divergent correlation lengths. In this work we adopt the ternary MERA scheme where three lattice sites at L τ are coarsegrained into a single site at L τ+1 .…”