Exact many-electron ground states on diamond and triangle Hubbard chains

TL;DR

This paper develops a method to construct exact ground states for interacting electrons on diamond and triangle Hubbard chains, revealing tunable magnetic and electronic properties without requiring integrability.

Contribution

It introduces a general approach to find exact ground states in Hubbard models using positive semidefinite Hamiltonian reformulation, applicable in any dimension and not relying on integrability.

Findings

Exact ground states constructed for diamond and triangle Hubbard chains.

Ground states exhibit flat-band ferromagnetism and diverse electronic behaviors.

Properties can be tuned by magnetic flux, potentials, or electron density.

Abstract

We construct exact ground states of interacting electrons on triangle and diamond Hubbard chains. The construction requires (i) a rewriting of the Hamiltonian into positive semidefinite form, (ii) the construction of a many-electron ground state of this Hamiltonian, and (iii) the proof of the uniqueness of the ground state. This approach works in any dimension, requires no integrability of the model, and only demands sufficiently many microscopic parameters in the Hamiltonian which have to fulfill certain relations. The scheme is first employed to construct exact ground state for the diamond Hubbard chain in a magnetic field. These ground states are found to exhibit a wide range of properties such as flat-band ferromagnetism and correlation induced metallic, half-metallic or insulating behavior, which can be tuned by changing the magnetic flux, local potentials, or electron density. Detailed proofs of the uniqueness of the ground states are presented. By the same technique exact ground states are constructed for triangle Hubbard chains and a one-dimensional periodic Anderson model with nearest-neighbor hybridization. They permit direct comparison with results obtained by variational techniques for f-electron ferromagnetism due to a flat band in CeRh3B2.