https://doi.org/10.1140/epjb/s10051-026-01197-0
Research - Condensed Matter
Doping and temperature dependence of pairing correlations in the two-dimensional Hubbard model: a determinant quantum Monte Carlo study
Department of Physics, Amity Institute of Applied Sciences, Amity University Kolkata, Major Arterial Road, Action Area II, 700135, Kolkata, West Bengal, India
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Received:
21
April
2026
Accepted:
1
June
2026
Published online:
14
June
2026
Abstract
We investigate superconducting pairing correlations in the doped two-dimensional Hubbard model using determinant quantum Monte Carlo simulations at intermediate coupling (
). By systematically analyzing magnetic, vertex, symmetry-resolved, real-space, and finite-size pairing diagnostics as functions of doping and temperature, we obtain a coherent and cross-validated picture of interaction-driven pairing tendencies in the accessible parameter regime. We find that antiferromagnetic correlations are rapidly suppressed with hole doping, accompanied by a systematic enhancement of d-wave pairing correlations. The vertex contribution in the d-wave channel exhibits a crossover from negative to positive values upon doping, indicating a transition from an effectively repulsive to an attractive interaction. Symmetry-resolved analysis identifies the d-wave channel as the dominant interaction-driven pairing channel, while real-space correlations and finite-size scaling demonstrate that pairing remains short-ranged within the accessible temperatures and system sizes. The temperature dependence of pairing correlations reveals a nontrivial, non-monotonic interplay with doping, with enhanced pairing tendencies at intermediate doping levels. By combining vertex analysis, symmetry-resolved correlations, real-space behavior, and finite-size scaling within a unified framework, we provide a consistent cross-validation of interaction-driven pairing across multiple observables. Despite the enhancement of pairing correlations with decreasing temperature, no clear signatures of long-range superconducting order are observed. These results support a picture of interaction-driven d-wave pairing tendencies mediated by spin fluctuations and enhanced by hole doping, while highlighting the persistence of strong pairing fluctuations without long-range coherence in the accessible regime.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjb/s10051-026-01197-0.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
