A doubly-periodic structure for the study of inhomogeneous bulk fermion matter with spatial localizations

TL;DR

This paper introduces a novel method using doubly-periodic structures and localized states to perform fully antisymmetrized simulations of inhomogeneous bulk fermion matter, enabling efficient and accurate analysis of spatial localization phenomena.

Contribution

The paper presents a new computational approach employing doubly-periodic structures and localized single-particle states for fully antisymmetrized bulk fermion simulations, improving efficiency and accuracy.

Findings

Reproduces essential fermion features effectively.

Uses circulant matrices for computational efficiency.

Applicable to inhomogeneous bulk fermion systems.

Abstract

We present a method that offers perspectives to perform fully antisymmetrized simulations for inhomogeneous bulk fermion matter. The technique bears resemblance to classical periodic boundary conditions, using localized single-particle states. Such localized states are an ideal tool to discuss phenomena where spatial localization plays an important role. The antisymmetrisation is obtained introducing a doubly-periodic structure in the many-body fermion wave functions. This results in circulant matrices for the evaluation of expectation values, leading to a computationally tractable formalism to study fully antisymmetrized bulk fermion matter. We show that the proposed technique is able to reproduce essential fermion features in an elegant and computationally advantageous manner.