The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

TL;DR

This paper studies the properties of charge and spin-neutral fermions in a square-lattice quantum liquid described by the Hubbard model, providing insights relevant for cold atom experiments and revealing a Fermi-liquid-like behavior.

Contribution

It introduces a rotated-electron framework for analyzing the Hubbard model, elucidating the momentum, energy, and velocity characteristics of charge and spin-neutral fermions in the one- and two-electron subspace.

Findings

Momentum bands and dispersions are characterized for charge c and spin-neutral s1 fermions.

The model exhibits residual interactions due to good quantum numbers in the subspace.

The approach simplifies the many-electron problem to a Fermi-liquid-like quantum liquid.

Abstract

The momentum bands, energy dispersions, and velocities of the charge $c$ fermions and spin-neutral two-spinon $s1$ fermions of a square-lattice quantum liquid referring to the Hubbard model on such a lattice of edge length $L$ in the one- and two-electron subspace are studied. The model involves the effective nearest-neighbor integral $t$ and on-site repulsion $U$ and can be experimentally realized in systems of correlated ultra-cold fermionic atoms on an optical lattice and thus our results are of interest for such systems. Our investigations profit from a general rotated-electron description, which is consistent with the model global $SO(3)\times SO(3)\times U(1)$ symmetry. For the model in the one- and two-electron subspace the discrete momentum values of the $c$ and $s1$ fermions are good quantum numbers so that in contrast to the original strongly-correlated electronic problem their interactions are residual. The use of our description renders an involved many-electron problem into a quantum liquid with some similarities with a Fermi liquid.