Magnetic properties of alternating Hubbard ladders

TL;DR

This study uses DMRG to analyze the magnetic properties of alternating Hubbard ladders, revealing long-range ferrimagnetic order and how alternation affects magnetic behavior in quasi-one-dimensional systems.

Contribution

It provides detailed numerical evidence of ferrimagnetic order in alternating Hubbard ladders, extending Lieb's theorem to these geometries and exploring effects on magnetic phases.

Findings

Existence of long-range ferrimagnetic order in alternating ladders

Quantitative analysis of excitation gaps and correlation functions

Impact of alternation pattern on magnetic phase behavior

Abstract

We investigate the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite, with a non-equal number of sites on the two sublattices. Thus they share a key feature of the Hubbard model in a class of lattices which Lieb has shown analytically to exhibit long-range ferrimagnetic order, while being amenable to powerful numeric approaches developed for quasi-one-dimensional geometries. The Density Matrix Renormalization Group (DMRG) method is used to obtain the ground state properties, e.g. excitation gaps, charge and spin densities as well as their correlation functions at half-filling. We show the existence of long-range ferrimagnetic order in the one-dimensional ladder geometries. Our work provides detailed quantitative results which complement the general theorem of Lieb for generalized bipartite lattices. It also addresses the issue of how the alternation between quasi-long range order and spin liquid behavior for uniform ladders with odd and even numbers of legs might be affected by a regular alternation pattern.