Fulde-Ferrell-Larkin-Ovchinnikov critical polarization in one-dimensional fermionic optical lattices

TL;DR

This paper derives an analytical expression for the critical polarization threshold for FFLO state emergence in one-dimensional fermionic lattices, providing a phase diagram and confirming the universality of the upper bound across various conditions.

Contribution

It introduces a universal analytical expression for the critical polarization in 1D fermionic lattices and maps phase diagrams for confined systems.

Findings

Critical polarization P_C^{max}=1/3 is universal across densities and interactions.

Phase diagram of FFLO state depends on polarization, interaction, and density.

Analytical and numerical methods confirm the universality of the critical polarization bound.

Abstract

We deduce an expression for the critical polarization P_C below which the FFLO-state emerges in one-dimensional lattices with spin-imbalanced populations. We provide and explore the phase diagram of unconfined chains as a function of polarization, interaction and particle density. For harmonically confined systems we supply a quantitative mapping which allows to apply our phase diagram also for confined chains. We find analytically, and confirm numerically, that the upper bound for the critical polarization is universal: P_C^{max}=1/3 for any density, interaction and confinement strength.