{
  "abstract": "Building on the recently developed tensor-backflow method, which accurately describes energies and stripe states in the Fermi-Hubbard model, we investigate $d$-wave pairing in the two-dimensional $t$-$t'$-$U$ Hubbard model. For the $8\\times8$ lattice, we improve the wave function using symmetry projections followed by one Lanczos step, whereas for the $12\\times 12$ and $16\\times 16$ lattices, we apply one Lanczos step without symmetry projection. We focus primarily on the parameter regime with filling $n=0.875$, on-site repulsion $U=8$ and next-nearest-neighbor hopping $t'=-0.2t$, a regime in which enhanced $d$-wave pairing has been reported. The resulting energies are competitive with those obtained using state-of-the-art neural quantum states. For example, on a $16\\times 16$ lattice with periodic boundary conditions, the tensor-backflow wave function after one Lanczos step without explicit symmetry enforcement achieves a relative energy difference of $4.4\\times 10^{-3}$ from the symmetry-preserving neural quantum state result. From the real space pair correlations, for $t'=-0.2t$, we observe stronger $d$-wave pair correlations together with the characteristic relative sign between horizontal and vertical bond-pair components. Compared with $t'=0$, finite negative $t'$ increases the spectral weight of the corresponding pair-density matrix, which indicates the enhanced overall $d$-wave pair fluctuations. The leading eigenvalue is enhanced on the $8\\times8$ lattice for both with and without symmetry projections. For larger lattices such as $12\\times 12$ and $16\\times 16$, the leading pair-density matrix spectral weight is distributed among several nearly degenerate eigenmodes rather than being concentrated in a single dominant mode. This indicates enhanced and more broadly distributed $d$-wave pair fluctuations, but no single eigenvalue exhibits the extensive scaling required for ODLRO.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22618",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiao Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bxc9p7ymvytm9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22618",
  "fulltext_url": null,
  "id": "bxc9p7ymvytm9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22618",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "cond-mat.supr-con"
    ],
    [
      "openalex",
      "3104|Physics of Superconductivity and Magnetism"
    ]
  ],
  "openalex": "W7214040749",
  "pdf_url": "https://arxiv.org/pdf/2609.22618",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bxc9p7ymvytm9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.22618",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22618"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Probing $d$-wave pairing in the $t$-$t'$-$U$ Hubbard model with tensor-backflow wave functions",
  "title_text": "Probing d-wave pairing in the t-t'-U Hubbard model with tensor-backflow wave functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/bxc9p7ymvytm9",
  "venue": "arXiv",
  "versions": []
}