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arXiv:2308.06497

Entangled magnetic, charge, and superconducting pairing correlations in the two-dimensional Hubbard model: a functional renormalization-group analysis

Sarah Heinzelmann, A. Toschi, Sabine Andergassen

Published Aug 12, 2023• 0 citations
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Abstract

Using the recently introduced multiloop extension of the functional renormalization group, we compute the magnetic, density, and superconducting susceptibilities of the two-dimensional Hubbard model at weak coupling and present a detailed analysis of their evolution with temperature, interaction strength, and loop order. By breaking down the susceptibilities into contributions from the bare susceptibility and the individual channels, we investigate their relative importance as well as the channel interplay. In particular, we trace the influence of antiferromagnetic fluctuations on the $d$-wave superconductivity and provide an analytical understanding for the observed behavior.

DOI
10.48550/arxiv.2308.06497

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The interplay and competition of magnetic and superconducting correlations in the weakly interacting two-dimensional Hubbard Model is investigated by means of the functional renormalization group. At zero temperature the flow of interactions in one-loop approximation evolves into a strong coupling regime at low energy scales, signalling the possible onset of spontaneous symmetry breaking. This is further analyzed by a mean-field treatment of the strong renormalized interactions which takes into account magnetic and superconducting order simultaneously. The effect of strong correlations on single-particle properties in the normal phase is studied by calculating the flow of the self-energy. 1
The repulsive two-dimensional Hubbard model is analysed within a functional renormalisation group (RG) approach. The flow equation for the effective interactions is evaluated on 1-loop level. The effective interactions diverge at a finite energy scale which is exponentially small for small bare interactions. To analyse the nature of the instabilities signalled by the diverging interactions, we compute the flow of the superconducting susceptibilities for various pairing symmetries and also charge and spin density susceptibilities. Depending on the choice of the model parameters (hopping amplitudes, interaction strength and band-filling) we find spin density wave instabilities or d-wave superconductivity as leading instability close to half-filling. This calculation establishes the existence of d-wave superconductivity in the Hubbard model beyond doubt.
Abstract The interplay and competition of magnetic and superconducting correlations in the weakly interacting two‐dimensional Hubbard Model is investigated by means of the functional renormalization group. At zero temperature the flow of interactions in one‐loop approximation evolves into a strong coupling regime at low energy scales, signalling the possible onset of spontaneous symmetry breaking. This is further analyzed by a mean‐field treatment of the strong renormalized interactions which takes into account magnetic and superconducting order simultaneously. The effect of strong correlations on single‐particle properties in the normal phase is studied by calculating the flow of the self‐energy. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The phases with spontaneously broken symmetries corresponding to antiferromagnetic and ddd-wave superconducting order in the two-dimensional $t\ensuremath{-}{t}^{'}$-Hubbard model are investigated by means of the functional renormalization group. The introduction of composite boson fields in the magnetic, charge density, and superconducting channels allows an efficient parametrization of the four-fermion vertex and the study of regimes where either the antiferromagnetic or superconducting order parameter, or both, are nonzero. We compute the phase diagram and the temperature dependence of the order parameter below the critical temperature, where antiferromagnetic and superconducting order show a tendency of mutual exclusion.