Entanglement entropy and fidelity susceptibility in the one-dimensional spin-1 XXZ chains with alternating single-site anisotropy

TL;DR

This paper investigates how fidelity susceptibility and entanglement entropy reveal quantum phase transitions in a one-dimensional spin-1 XXZ chain with alternating single-site anisotropy, using numerical methods.

Contribution

It provides a detailed numerical analysis of the relationship between fidelity susceptibility, entanglement entropy, and quantum phase transitions in the spin-1 XXZ chain with anisotropy.

Findings

Fidelity susceptibility characterizes the phase transition from Haldane to Néel phase.

Finite size scaling shows a power-law divergence at criticality, indicating a second-order transition.

Entanglement entropy and Schmidt gap corroborate the phase transition analysis.

Abstract

We study the fidelity susceptibility in an antiferromagnetic spin-1 XXZ chain numerically. By using the density-matrix renormalization group method, the effects of the alternating single-site anisotropy $D$ on fidelity susceptibility are investigated. Its relation with the quantum phase transition is analyzed. It is found that the quantum phase transition from the Haldane spin liquid to periodic N\'{e}el spin solid can be well characterized by the fidelity. Finite size scaling of fidelity susceptibility shows a power-law divergence at criticality, which indicates the quantum phase transition is of second order. The results are confirmed by the second derivative of the ground-state energy. We also study the relationship between the entanglement entropy, the Schmidt gap and quantum phase transitions. Conclusions drawn from these quantum information observables agree well with each other.