Quantum Vorticity at positive temperature for spin systems with continuous symmetry

TL;DR

This paper introduces a quantum definition of vorticity at positive temperature for spin systems with continuous symmetry, supported by numerical simulations showing vortex patterns.

Contribution

It proposes a novel quantum vorticity concept for Gibbs states in spin systems and demonstrates its effectiveness through numerical simulations.

Findings

Numerical simulations reveal classical vortex patterns in quantum XY models.

The proposed vorticity definition aligns with classical intuition at positive temperature.

The approach bridges quantum and classical descriptions of vortices in spin systems.

Abstract

We propose a definition of vorticity at inverse temperature $\beta$ for Gibbs states in quantum XY or Heisenberg spin systems on the lattice by testing $\exp[-\beta H]$ on a complete set of observables ("one-point functions"). Imposing a compression of Pauli matrices at the boudary, which stands for the classical environment, we perform some numerical simulations on finite lattices in case of XY model, which exhibit usual vortex patterns.