Reduced fidelity approach for quantum phase transitions in spin-1/2 dimerized Heisenberg chains

TL;DR

This paper demonstrates that reduced fidelity susceptibility effectively detects second-order quantum phase transitions in spin-1/2 dimerized Heisenberg chains, offering a practical indicator that outperforms traditional energy derivatives.

Contribution

The study introduces reduced fidelity susceptibility as a more sensitive indicator for quantum phase transitions in spin chains, establishing its relation to energy derivatives and confirming its broad applicability.

Findings

Reduced fidelity susceptibility signals second-order phase transitions.

It is related to the second derivative of ground-state energy.

The method applies to systems with SU(2) and translation symmetries.

Abstract

We use reduced fidelity approach to characterize quantum phase transitions in the one-dimensional spin-1/2 dimerized Heisenberg chain in the antiferromagnetic case. The reduced fidelity susceptibilities between two nearest-neighboring spin pairs are considered. We find that they are directly related to the square of the second derivative of the ground-state energy. This enables us to conclude that the former might be a more effective indicator of the second-order quantum phase transitions than the latter. Two further exemplifications are given to confirm the conclusion is available for a broad class of systems with SU(2) and translation symmetries. Moreover, a general connection between reduced fidelity susceptibility and quantum phase transitions is illustrated.