Symmetric Hubbard Systems with Superconducting Magnetic Response

TL;DR

This paper demonstrates that Hubbard clusters with W=0 pairs exhibit genuine superconducting flux quantization, showing a magnetic response characteristic of superconductivity through detailed numerical analysis of mesoscopic rings.

Contribution

It introduces a cell-perturbation theory approach and an exact diagonalization technique to study superconducting magnetic response in Hubbard systems with W=0 pairs.

Findings

W=0 pairs lead to superconducting flux quantization in Hubbard rings.

Normal behavior observed at lower fillings.

Effective bosonic model describes itinerant pairs and SFQ.

Abstract

In purely repulsive, $C_{4v}$-symmetric Hubbard clusters a correlation effect produces an effective two-body attraction and pairing; the key ingredient is the availability of W=0 pairs, that is, two-body solutions of appropriate symmetry. We study the tunneling of bound pairs in rings of 5-site units connected by weak intercell links; each unit has the topology of a CuO$_{4}$ cluster and a repulsive interaction is included on every site. Further, we test the superconducting nature of the response of this model to a threading magnetic field. We present a detailed numerical study of the two-unit ring filled with 6 particles and the three-unit ring with 8 particles; in both cases a lower filling yields normal behavior. In previous studies on 1d Hubbard chains, level crossings were reported (half-integer or fractional Aharonov-Bohm effect) which however cannot be due to superconducting pairs. In contrast, the nontrivial basis of clusters carrying W=0 pairs leads to genuine Superconducting Flux Quantization (SFQ). The data are understood in terms of a cell-perturbation theory scheme which is very accurate for weak links. This low-energy approach leads to an effective hard core boson Hamiltonian which naturally describes itinerant pairs and SFQ in mesoscopic rings. For the numerical calculations, we take advantage of a recently proposed exact diagonalization technique which can be generally applied to many-fermion problems and drastically reduces the size of the matrices to be handled.