Ground-state two-spinon bonds in the Hubbard model on a square lattice

TL;DR

This paper investigates the ground and excited states of the Hubbard model on a square lattice using a rotated-electron framework, revealing insights into spin configurations and correlations relevant to high-temperature superconductors and cold atom systems.

Contribution

It introduces a rotated-electron description with good quantum numbers for occupancy, and characterizes spin configurations via spinon occupancy on an effective lattice, advancing understanding of electronic correlations.

Findings

Confirmed the role of spinon configurations in the spin spectrum.

Linked results to the physics of La$_2$CuO$_4$ and cold atom systems.

Provided a detailed description of spin-neutral bond particles.

Abstract

In this paper the spin configurations of the ground state and one- and two-electron excited states of the Hubbard model on the square lattice are studied. We profit from a general rotated-electron description, which is consistent with the model global $SO(3)\times SO(3)\times U(1)$ symmetry. For rotated electrons, doubly and single occupancy are good quantum numbers for on-site repulsion $U>0$. The above states are within that description generated by occupancy configurations of charge $c$ fermions and spin-singlet two-spinon $s1$ bond particles. Those describe the charge and spin degrees of freedom, respectively, of the rotated electrons that singly occupy sites. While the $c$ fermions have no internal structure, that of the spin-neutral $s1$ bond-particle occupancy configurations is here described in terms of spinon occupancies of a well-defined effective spin lattice. In reference \cite{companion} it is confirmed that our results contribute to the further understanding of the role of electronic correlations in the spin spectrum of the parent compound La$_2$CuO$_4$. They are also of interest for studies of ultra-cold fermionic atoms on an optical lattice.