Strong Boundary and Trap Potential Effects on Emergent Physics in Ultra-Cold Fermionic Gases

TL;DR

This paper investigates how boundary conditions and trap potentials influence emergent phases, especially superconductivity, in 2D fermionic gases using a novel renormalization group method, highlighting the importance of system size and trap shape.

Contribution

It introduces a real-space truncated unity functional renormalization group approach to systematically study trap and boundary effects in 2D Hubbard models.

Findings

Trap potential and system size significantly affect superconducting phases.

Lower temperatures are required to observe emergent phases in experiments.

Trap shape influences the realization of quantum phases.

Abstract

The field of quantum simulations in ultra-cold atomic gases has been remarkably successful. In principle it allows for an exact treatment of a variety of highly relevant lattice models and their emergent phases of matter. But so far there is a lack in the theoretical literature concerning the systematic study of the effects of the trap potential as well as the finite size of the systems, as numerical studies of such non periodic, correlated fermionic lattices models are numerically demanding beyond one dimension. We use the recently introduced real-space truncated unity functional renormalization group to study these boundary and trap effects with a focus on their impact on the superconducting phase of the 2D Hubbard model. We find that in the experiments not only lower temperatures need to be reached compared to current capabilities, but also system size and trap potential shape play a crucial role to simulate emergent phases of matter.