[Paper Review] Extended bound states of fermions on 2D square lattice beyond the nn hopping and interactions

M. Bąk, R. Micnas|arXiv (Cornell University)|Sep 6, 1999

Cold Atom Physics and Bose-Einstein Condensates3 citations

TL;DR

This paper investigates extended bound states of fermions in a 2D square lattice beyond nearest-neighbor (nn) hopping and interactions, using an exact two-body solution in the dilute limit of the extended Hubbard model. It demonstrates that next-nearest-neighbor (nnn) hopping strongly favors d-wave pairing, leading to deep bound states with nontrivial dispersion across the Brillouin zone and evidence of s*-d symmetry mixing.

ABSTRACT

We examine extended bound states in the dilute limit of the extended Hubbard model with next-nearest-neighbour (nnn) hopping and nnn interactions on the two dimensional square lattice. By the exact solution of a two-body problem we show that d-wave pairing is strongly favored by the nnn hopping. We determine the binding energies, mobilities and dispersion curves across Brillouin zone (B.z.) for bound states of various symmetries. The numerical analysis shows that the deep bound states can exist in the whole B.z. and we have also found s*-d mixing of the bound states.

Motivation & Objective

• To investigate the formation of extended bound states in a 2D square lattice beyond nearest-neighbor hopping and interactions.
• To determine the role of next-nearest-neighbor (nnn) hopping and interactions in stabilizing pairing channels.
• To analyze the binding energies, mobilities, and dispersion relations of bound states across the Brillouin zone.
• To explore symmetry mixing, particularly s*-d mixing, in the bound state spectrum.
• To establish the conditions under which deep bound states can exist in the whole Brillouin zone.

Proposed method

• Exact solution of the two-body problem within the extended Hubbard model on a 2D square lattice.
• Incorporation of both next-nearest-neighbor (nnn) hopping and nnn interactions in the Hamiltonian.
• Numerical analysis of bound state properties, including binding energy, mobility, and dispersion curves.
• Evaluation of the full momentum-space dependence of bound states across the Brillouin zone.
• Use of symmetry analysis to identify and characterize s*-d mixing in the bound state wavefunctions.
• Application of exact diagonalization techniques to solve the two-body Schrödinger equation in the lattice model.

Experimental results

Research questions

• RQ1 How does next-nearest-neighbor (nnn) hopping influence the formation of bound states in a 2D fermionic lattice?
• RQ2 What is the role of nnn interactions in stabilizing d-wave pairing in the extended Hubbard model?
• RQ3 Can deep bound states exist across the entire Brillouin zone under the influence of nnn hopping?
• RQ4 To what extent do s- and d-wave symmetries mix in the bound state wavefunctions?
• RQ5 How do the binding energies and mobilities of bound states vary across different momentum points in the Brillouin zone?

Key findings

• Next-nearest-neighbor (nnn) hopping strongly favors d-wave pairing in the extended Hubbard model on a 2D square lattice.
• Deep bound states are found to exist across the entire Brillouin zone, indicating robust pairing across momentum space.
• The binding energies of these bound states are significant and exhibit nontrivial dispersion relations throughout the Brillouin zone.
• Numerical results reveal clear evidence of s*-d mixing in the wavefunctions of the bound states, indicating hybridization of symmetry channels.
• Mobility of the bound states is finite and varies with momentum, suggesting they are not localized but delocalized across the lattice.
• The existence of bound states with non-zero momentum and strong pairing character supports the potential for unconventional superconductivity in such systems.