General Quantum Fidelity Susceptibilities for the J1-J2 Chain

TL;DR

This paper investigates generalized quantum fidelity susceptibilities in the J1-J2 Heisenberg chain, demonstrating their effectiveness in detecting the Berezinskii-Kosterlitz-Thouless quantum phase transition at J2 ≈ 0.241J1.

Contribution

It introduces and analyzes three specific fidelity susceptibilities related to different order parameters, showing their ability to accurately identify a complex quantum critical point.

Findings

All three susceptibilities detect the critical point at J2 ≈ 0.241J1.

They successfully distinguish between gapless and dimerized phases.

The susceptibilities are sensitive to the phase diagram and critical behavior.

Abstract

We study slightly generalized quantum fidelity susceptibilities where the differential change in the fidelity is measured with respect to a different term than the one used for driving the system towards a quantum phase transition. As a model system we use the spin-1/2 J1-J2 antiferromagnetic Heisenberg chain. For this model, we study three fidelity susceptibilities, chi_p, chi_D and chi_AF, which are related to the spin stiffness, the dimer order and antiferromagnetic order, respectively. All these ground-state fidelity susceptibilities are sensitive to the phase diagram of the J1-J2 model. We show that they all can accurately identify a quantum critical point in this model occurring at J2 = 0.241J1 between a gapless Heisenberg phase for J2 < J2_critical and a dimerized phase for J2 > J2_critical. This phase transition, in the Berezinskii-Kosterlitz-Thouless universality class, is controlled by a marginal operator and is therefore particularly difficult to observe.