Interaction-Induced Gradients Across a Confined Fermion Lattice

TL;DR

This study investigates how an imposed chemical potential gradient on one fermionic species induces a density gradient in a second species through interactions, revealing conditions for equal gradients and magnetic correlations in a confined lattice.

Contribution

It demonstrates how interactions induce density gradients in a second fermionic species without a direct chemical potential gradient, and explores the resulting magnetic correlations and ferromagnetic behavior.

Findings

Density gradient in second species grows with interaction strength U.

At a critical U*, the two species have equal density gradients.

Antiferromagnetism peaks at half-filled densities, and ferromagnetism emerges with large gradients.

Abstract

An imposed chemical potential gradient $A_\uparrow=d\mu_\uparrow/dx$ on a single fermionic species ("spin up") directly produces a gradient in the density $d\rho_\uparrow/dx$ across a lattice. We study here the induced density inhomogeneity $d\rho_\downarrow/dx$ in the second fermionic species ("spin down") which results from fermionic interactions $U$, even in the absence of a chemical potential gradient $A_\downarrow=0$ on that species. The magnitude of $d\rho_\downarrow/dx$ acquired by the second species grows with $U$, while the magnitude of $d\rho_\uparrow/dx$ remains relatively constant, that is, set only by $A_\uparrow$. For a given $A_\uparrow$, we find an interaction strength $U_*$ above which the two density gradients are equal in magnitude. We also evaluate the spin-spin correlations and show that, as expected, antiferromagnetism is most dominant at locations where the local density is half-filled. The spin polarization induced by sufficiently large gradients, in combination with $U$, drives ferromagnetic behavior. In the case of repulsive interactions, $d\rho_\downarrow/dx = -d\rho_\uparrow/dx$. A simple particle-hole transformation determines the related effect in the case of attractive interactions.