Superconductivity in the two-dimensional Hubbard model revealed by neural quantum states

Fuente: arXiv
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Main Authors: Roth, Christopher, Chen, Ao, Sengupta, Anirvan, Georges, Antoine
Format: Preprint
Published: 2025
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author Roth, Christopher
Chen, Ao
Sengupta, Anirvan
Georges, Antoine
author_facet Roth, Christopher
Chen, Ao
Sengupta, Anirvan
Georges, Antoine
contents Whether the ground state of the square lattice Hubbard model exhibits superconductivity remains a major open question, central to understanding high temperature cuprate superconductors and ultra-cold fermions in optical lattices. Numerical studies have found evidence for stripe-ordered states and superconductivity at strong coupling but the phase diagram remains controversial. Here, we show that one can resolve the subtle energetics of metallic, superconducting, and stripe phases using a new class of neural quantum state (NQS) wavefunctions that extend hidden fermion determinant states to Pfaffians. We simulate several hundred electrons using fast Pfaffian algorithms allowing us to measure off-diagonal long range order. At strong coupling and low hole-doping, we find that a non-superconducting filled stripe phase prevails, while superconductivity coexisting with partially-filled stripes is stabilized by a negative next neighbor hopping t-prime, with |t-prime| > 0.1. At larger doping levels, we introduce momentum-space correlation functions to mitigate finite size effects that arise from weakly-bound pairs. These provide evidence for uniform d-wave superconductivity at U = 4, even when t-prime = 0. Our results highlight the potential of NQS approaches, and provide a fresh perspective on superconductivity in the square lattice Hubbard model.
format Preprint
id arxiv_https___arxiv_org_abs_2511_07566
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Superconductivity in the two-dimensional Hubbard model revealed by neural quantum states
Roth, Christopher
Chen, Ao
Sengupta, Anirvan
Georges, Antoine
Superconductivity
Disordered Systems and Neural Networks
Strongly Correlated Electrons
Whether the ground state of the square lattice Hubbard model exhibits superconductivity remains a major open question, central to understanding high temperature cuprate superconductors and ultra-cold fermions in optical lattices. Numerical studies have found evidence for stripe-ordered states and superconductivity at strong coupling but the phase diagram remains controversial. Here, we show that one can resolve the subtle energetics of metallic, superconducting, and stripe phases using a new class of neural quantum state (NQS) wavefunctions that extend hidden fermion determinant states to Pfaffians. We simulate several hundred electrons using fast Pfaffian algorithms allowing us to measure off-diagonal long range order. At strong coupling and low hole-doping, we find that a non-superconducting filled stripe phase prevails, while superconductivity coexisting with partially-filled stripes is stabilized by a negative next neighbor hopping t-prime, with |t-prime| > 0.1. At larger doping levels, we introduce momentum-space correlation functions to mitigate finite size effects that arise from weakly-bound pairs. These provide evidence for uniform d-wave superconductivity at U = 4, even when t-prime = 0. Our results highlight the potential of NQS approaches, and provide a fresh perspective on superconductivity in the square lattice Hubbard model.
title Superconductivity in the two-dimensional Hubbard model revealed by neural quantum states
topic Superconductivity
Disordered Systems and Neural Networks
Strongly Correlated Electrons
url https://arxiv.org/abs/2511.07566