Quantum phase transition by employing trace distance along with the density matrix renormalization group

TL;DR

This paper introduces a novel approach combining trace distance with DMRG to detect quantum phase transitions at finite temperatures, demonstrating its effectiveness on spin chains by identifying critical points through correlation discontinuities.

Contribution

The study presents a new method using trace distance within DMRG to detect quantum criticality, applicable at finite temperatures, enhancing existing techniques.

Findings

Trace distance detects critical points via discontinuities.

Method successfully applied to spin-1 XXZ and Heisenberg chains.

Effective at finite temperature quantum phase transition detection.

Abstract

We use an alternative method to investigate the quantum criticality at zero and finite temperature using trace distance along with the density matrix renormalization group. It is shown that the average correlation measured by the trace distance between the system block and environment block in a DMRG sweep is able to detect the critical points of quantum phase transitions at finite temperature. As illustrative examples, we study spin-1 XXZ chains with uniaxial single-ion-type anisotropy and the Heisenberg spin chain with staggered coupling and external magnetic field. It is found that the trace distance shows discontinuity at the critical points of quantum phase transition and can be used as an indicator of QPTs.