Entanglement renormalization of anisotropic XY model

TL;DR

This paper applies multiscale entanglement renormalization ansatz to analyze the phase transitions and entanglement properties of the anisotropic XY model, demonstrating improved accuracy with larger truncation and block sizes.

Contribution

It introduces optimized disentanglers that effectively reduce short-range entanglement, enhancing the accuracy of phase boundary and critical exponent calculations in the XY model.

Findings

Disentanglers remove short-range entanglement effectively.

Larger truncation dimensions improve result accuracy.

Increasing block size or look-ahead step enhances calculation consistency.

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.