Quantum critical surface of the zigzag spin chain under magnetic field: Application to superconducting quantum dots

TL;DR

This paper investigates the quantum critical surface of the XXZ zigzag spin chain under magnetic field, deriving an analytical expression applicable to superconducting quantum dots, and identifies ground states using mathematical theorems and Bethe ansatz.

Contribution

It provides the first analytical expression for the quantum critical surface in superconducting quantum dots with gate voltage, linking spin chain models to quantum dot systems.

Findings

Identified the quantum critical surface using positive semi-definite matrix theorem.

Proved ground states are fully polarized and one magnon states within certain regions.

Derived analytical expression for quantum critical surface in superconducting quantum dots.

Abstract

We analyze the exact ground state of XXZ zigzag spin chain with applied magnetic field and find the quantum critical surface. Using the theorem of positive semi-definite matrix, we can prove that the ground states for a specific region, are fully polarized state and one magnon states. With Bethe ansatz, we argue that this is the quantum critical surface in all cases. A first in the literature, we derive the analytical expression of quantum critical surface for superconducting quantum dots array in the presence of gate voltage.