Composite quasiparticle formation and the low-energy effective Hamiltonians of the one- and two-dimensional Hubbard Model

TL;DR

This paper explores how hole doping affects the low-energy quasiparticle excitations in the strongly-coupled Hubbard model across one and two dimensions, revealing different soliton behaviors and deriving effective Hamiltonians.

Contribution

It introduces a unified approach to derive effective Hamiltonians for doped Hubbard models, highlighting the dimensional dependence of soliton properties.

Findings

In 1D, solitons are topological and spinless, decoupled from fluctuations.

In 2D, solitons are non-topological with spin 1/2, strongly coupled to fluctuations.

Derived effective actions for quasiparticle motion and analyzed single carrier properties.

Abstract

We investigate the effect of hole doping on the strong-coupling Hubbard model at half-filling in spatial dimensions $D\ge 1$. We start with an antiferromagnetic mean-field description of the insulating state, and show that doping creates solitons in the antiferromagnetic background. In one dimension, the soliton is topological, spinless, and decoupled from the background antiferromagnetic fluctuations at low energies. In two dimensions and above, the soliton is non-topological, has spin quantum number 1/2, and is strongly coupled to the antiferromagnetic fluctuations. We derive the effective action governing the quasiparticle motion, study the properties of a single carrier, and comment on a possible description at finite concentration.