Low-energy effective theory at a quantum critical point of the two-dimensional Hubbard model

• Verfasst von: Veschgini, Kambis [VerfasserIn]
• Verfasst von: Salmhofer, Manfred [VerfasserIn]
• Titel: Low-energy effective theory at a quantum critical point of the two-dimensional Hubbard model
• Titelzusatz: mean-field analysis
• Verf.angabe: Kambis Veschgini and Manfred Salmhofer
• E-Jahr: 2018
• Jahr: 31 Aug 2018
• Umfang: 16 S.
• Fussnoten: Gesehen am 06.11.2020
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2018
• Band/Heft Quelle: (2018) Artikel-Nummer 1806.08930, 16 Seiten
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Condensed Matter - Strongly Correlated Electrons
• K10plus-PPN: 1585789011

Abstract

We complement previous functional renormalization group (fRG) studies of the two-dimensional Hubbard model by mean-field calculations. The focus falls on Van Hove filling and the the hopping amplitude t'/t=0.341. The fRG data suggest a quantum critical point (QCP) in this region and in its vicinity a singular fermionic self-energy, Im $\Sigma(\omega)/\omega \sim |\omega|^{-\gamma}$ with $\gamma\approx 0.26$. Here we start a more detailed investigation of this QCP using a bosonic formulation for the effective action, where the bosons couple to the order parameter fields. To this end, we use the channel decomposition of the fermionic effective action developed in [Phys. Rev. B 79, 195125 (2009)], which allows to perform Hubbard-Stratonovich transformations for all relevant order parameter fields at any given energy scale. We stop the flow at a scale where the correlations of the order parameter field are already pronounced, but the flow is still regular, and derive the effective boson theory. It contains d-wave superconducting, magnetic, and density-density interactions. We analyze the resulting phase diagram in the mean-field approximation. We show that the singular fermionic self-energy suppresses gap formation both in the superconducting and magnetic channel already at the mean-field level, thus rounding a first-order transition (without self-energy) to a quantum phase transition (with self-energy). We give a simple effective model that shows the generality of this effect. In the two-dimensional Hubbard model, the effective density-density interaction is peaked at a nonzero frequency, so that solving the mean-field equations already involves a functional equation instead of simply a matrix equation (on a technical level, similar to incommensurate phases). Within a certain approximation, we show that such an interaction leads to a short quasiparticle lifetime.