Quantum vorticity at thermal equilibrium for spins systems with continuous symmetry

TL;DR

This paper introduces a quantum definition of vorticity at thermal equilibrium for XY spin systems, demonstrating basis independence and visualizing vortex patterns through numerical simulations on finite lattices.

Contribution

It proposes a novel quantum vorticity concept for Gibbs states in XY models, incorporating boundary conditions and numerical visualization of vortex structures.

Findings

Vorticity definition is basis-independent.

Numerical simulations reveal classical vortex patterns.

Boundary conditions influence vortex configurations.

Abstract

We propose a definition of vorticity at inverse temperature \beta for Gibbs states in quantum XY spin systems on the lattice by testing \exp[-\beta H] on a complete set of observables ("one-point functions"). We show in particular that it is independent of the choice of a particular basis. Imposing a compression of Pauli matrices at the boudary, which stands for the classical environment, we make some numerical simulations on finite lattices, and exhibit usual vortex patterns.