Navigating the phase diagram of quantum many-body systems in phase space

TL;DR

This paper explores how the Wigner function in phase space can be used to analyze phase diagrams of quantum spin chains, comparing its effectiveness with entanglement measures and highlighting the importance of system homogeneity.

Contribution

It introduces phase space methods for studying quantum phase diagrams and compares their effectiveness with traditional entanglement measures, revealing system homogeneity impacts.

Findings

Equal angle slice approximation captures key features but not negativity accurately.

Full phase space integration is necessary for inhomogeneous chains.

Phase space methods are sensitive to system homogeneity.

Abstract

We demonstrate the unique capabilities of the Wigner function, particularly in its positive and negative parts, for exploring the phase diagram of the spin$-(\frac{1}{2\!}-\!\frac{1}{2})$ and spin$-(\frac{1}{2}\!-\!1)$ Ising-Heisenberg chains. We highlight the advantages and limitations of the phase space approach in comparison with the entanglement concurrence in detecting phase boundaries. We establish that the equal angle slice approximation in the phase space is an effective method for capturing the essential features of the phase diagram, but falls short in accurately assessing the negativity of the Wigner function for the homogeneous spin$-(\frac{1}{2}\!-\!\frac{1}{2})$ Ising-Heisenberg chain. In contrast, we find for the inhomogeneous spin$-(\frac{1}{2}\!-\!1)$ chain that an integral over the entire phase space is necessary to accurately capture the phase diagram of the system. This distinction underscores the sensitivity of phase space methods to the homogeneity of the quantum system under consideration.