Spin and Charge Fluctuations Behind Strange Metallicity in the Hubbard Model [HBNI Th273]

Abstract

In this thesis, we investigated the Hubbard model in the strong coupling regime with a dual approach: an analytical treatment based on the limit of infinite onsite repulsion 𝑈 = ∞ in which we developed an approximate self-consistent approach, and a numerical treatment at finite 𝑈 using the Dynamical Mean Field Theory (DMFT) framework implemented with the Numerical Renormalization Group (NRG) as the impurity solver. The aim was to explore the nature of electron transport and fluctuation dynamics, particularly the crossover from coherent to incoherent regimes and to illuminate the underlying mechanisms driving anoma- lous transport behavior such as linear-in-𝑇 resistivity in correlated metals. In the first part, we developed a new ECFL-based self-consistent scheme in the 𝑈 = ∞ limit using the Hubbard 𝑋-operator formalism. Exploiting the simplifications that emerge in the infinite-dimensional (𝑑 → ∞) limit, we derived closed-form expressions for the Dysonian self-energy Σ as a convolution of the single-particle Green’s function 𝐺 with local charge and spin fluctuation correlators, 𝐷𝑁 and 𝐷𝑆 . These correlators were obtained by expressing them in terms of relevant current-current correlation function using equation of motion. The current-current correlations are in turn obtained by evaluating bubble diagram since the vertex corrections vanish in high dimensions (𝑑 = ∞). This formulation revealed how incoherent, site-local, and bosonic number and spin fluctuations dynamically affect electron propagation. A central result of the ECFL analysis was the emergence of a temperature-driven crossover from a coherent Fermi liquid to an incoherent quantum regime (IQR) followed by a “bad metal” regime. Also, we were able to identify energy scales differentiating the quantum and classical regimes of transport. We find that the 125IQR hosts linear resistivity in temperature and the resistivity is due to scattering of electrons due to incoherent quantum local charge fluctuations. This region is reminiscent of a strange metal. Since our treatment of infinite 𝑈 Hubbard model doesn’t differentiate between charge and spin fluctuation. In the second part of the thesis, we numerically studied the Hubbard model at finite 𝑈 within the DMFT framework using NRG as an impurity solver. In our study, we find that the spin fluctuations become classical at lower temperatures compared to charge fluctuations. In other words, a two-stage decoherence process emerges: spin incoherence precedes charge incoherence. This staggered incoherence leads to the breakdown of Fermi liquid behavior in stages, providing a microscopic basis for strange metallicity and bad metallic transport. To probe the nature of this crossover and the associated incoherence, we analyzed various metrics: characteristic frequency scales (Ω𝑛/𝑠 ), Kullback-Leibler diver- gence (KLD), kurtosis, and inverse diffusion constants. These observables not only confirmed the separation between spin and charge coherence scales but also allowed us to distinguish between quantum-coherent, quantum-incoherent, and classical transport regimes. Spin degrees of freedom were found to become classical at lower temperatures compared to charge, highlighting the differential decoherence and its imprint on transport properties. The kurtosis, in particular, showed drastically sharper features in spin fluctuations compared to charge, indicating a spin-dominated coherence scale. In the doped Mott insulator, our analysis uncovered isosbestic points (frequencies at which the response functions are invariant with temperature) in both spin and charge spectra suggesting sum-rule constraints or hidden conservation laws at play. These findings prompt further exploration of connections to Luttinger’s theorem, compressibility and moment sum rules, and the broader structure of spectral weight transfer across interaction and temperature regimes.