Renormalization of trace distance and multipartite entanglement close to the quantum phase transitions of one- and two-dimensional spin-chain systems

TL;DR

This paper explores how trace distance and multipartite entanglement can detect quantum phase transitions in 1D and 2D spin systems using a real-space renormalization approach, revealing universal scaling laws near critical points.

Contribution

It introduces a method combining trace distance and multipartite entanglement with real-space renormalization to identify quantum phase transitions in spin chains.

Findings

Quantum phase transitions are indicated by singularities in derivatives of renormalized trace distance and entanglement.

Renormalized measures follow universal exponential scaling laws near critical points.

The approach applies to both one- and two-dimensional XY models.

Abstract

We investigate the quantum phase transitions of spin systems in one and two dimensions by employing trace distance and multipartite entanglement along with real-space quantum renormalization group method. As illustration examples, a one-dimensional and a two-dimensional $XY$ models are considered. It is shown that the quantum phase transitions of these spin-chain systems can be revealed by the singular behaviors of the first derivatives of renormalized trace distance and multipartite entanglement in the thermodynamics limit. Moreover, we find the renormalized trace distance and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical points.