Quantum effects in nanosystems: good reasons to use phase-space Weyl symbols

TL;DR

This paper advocates for using phase-space Weyl symbols to analyze quantum effects in nanosystems, especially where translation symmetry is broken, offering a practical alternative to Bogoliubov transformations.

Contribution

It introduces a phase-space Weyl symbol approach for nanosystems, simplifying the analysis of quantum effects without relying on translation symmetry.

Findings

Effective in estimating quantum effects in nanoscopic systems

Applied to spin-flop transition in antiferromagnetic chains

Potentially useful for phase diagram analysis

Abstract

Bogoliubov transformations have been successfully applied in several Condensed Matter contexts, e.g., in the theory of superconductors, superfluids, and antiferromagnets. These applications are based on bulk models where translation symmetry can be assumed, so that few degrees of freedom in Fourier space can be `diagonalized' separately, and in this way it is easy to find the approximate ground state and its excitations. As translation symmetry cannot be invoked when it comes about nanoscopic systems, the corresponding multidimensional Bogoliubov transformations are more complicated. For bosonic systems it is much simpler to proceed using phase-space variables, i.e., coordinates and momenta. Interactions can be accounted for by the self-consistent harmonic approximation, which is naturally developed using phase-space Weyl symbols. The spin-flop transition in a short antiferromagnetic chain is illustrated as an example. This approach, rarely used in the past, is expected to be generally useful to estimate quantum effects, e.g., on phase diagrams of ordered vs disordered phases.