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Two-Dopant Origin of Competing Stripe and Pair Formation in Hubbard and t−J Models

Tizian Blatz1,2,*, Ulrich Schollwöck1,2, Fabian Grusdt1,2, and Annabelle Bohrdt1,2,3,†

  • *Contact author: blatz.tizian@physik.uni-muenchen.de
  • †Contact author: a.bohrdt@lmu.de
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Phys. Rev. X 15, 031074 – Published 24 September, 2025

DOI: https://doi.org/10.1103/dpfl-12st

Abstract

Understanding the physics of the two-dimensional Hubbard model is widely believed to be a key step in achieving a full understanding of high-Tc cuprate superconductors. In recent years, progress has been made by large-scale numerical simulations at finite doping and, on the other hand, by microscopic theories able to capture the physics of individual charge carriers. In this work, we study single pairs of dopants in a cylindrical system using the density-matrix renormalization group algorithm. We identify two coexisting charge configurations that couple to the spin environment in different ways: a tightly bound configuration featuring (next-)nearest-neighbor pairs and a stripelike configuration of dopants on opposite sides of the cylinder, accompanied by a spin domain wall. Thus, we establish that the interplay between stripe order and uniform pairing, central to the models’ phases at finite doping, has its origin at the single-pair level. By interpolating between the Hubbard and the related t−J model, we are able to quantitatively understand discrepancies in the pairing properties of the two models through the three-site hopping term usually omitted from the t−J Hamiltonian. This term is closely related to a next-nearest-neighbor tunneling t′, which we observe to upset the balance between the competing stripe and pair states on the two-dopant level.

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Popular Summary

High-temperature superconductors exhibit a complex competition between superconducting and insulating striped phases. Understanding this interplay is key to designing materials that conduct without resistance at practical temperatures. In our work, we discover that this competition can be observed at the scale of a single pair of charge carriers—challenging the long-held belief that many carriers are needed for such collective behaviors. This microscopic perspective marks a surprising and important step toward unraveling the mechanisms behind unconventional superconductivity.

We investigate this problem using advanced numerical simulations of mobile dopants moving in an antiferromagnetic background, a setting relevant to cuprate superconductors. By analyzing charge and magnetic correlations, we uncover two distinct types of charge pairing: one associated with uniform-density superconducting states and the other with insulating striped configurations. We find that these two types of pairs appear across the two most widely used theoretical models for the cuprates. This unifying insight helps resolve a major debate in the field over the nature of pairing in these materials.

Our results deepen our understanding of the building blocks of superconductivity and highlight a new direction for experimental investigation. In particular, we argue that quantum simulation platforms realizing the t−J model are well positioned to directly observe these pairing effects in the lab. This opens the door to experimentally probing the microscopic roots of high-temperature superconductivity.

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Outline

Information

Phys. Rev. X 15, 031074– Published 24 September, 2025
  • Received 22 October 2024
  • Revised 31 March 2025
  • Accepted 25 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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