Hubbard model at U=$\infty$: Role of single and two-boson fluctuations

Abstract

We have developed a semi-analytical framework formulated in the canonical fermion representation to investigate strongly correlated electron systems. We consider the U=$\infty$ Hubbard model and used the equation of motion method to calculate the fermion self-energy which has two parts: single and two-boson exchange processes. The emergent bosons here are self-generated local charge and spin-density fluctuations which become strongly time-dependent due to extreme correlations. The computed boson spectral density is a diffusive damped mode with a long tail. The electron self-energy at $d=\infty$ is computed self-consistently. The corresponding fermionic spectral density displays a pronounced coherence peak at $ω=0$, while its frequency derivative develops a two-peak structure at finite $ω$. The resistivity shows a linear temperature dependence over a broad range, crossing over to coherent Fermi-liquid behavior at extremely low temperatures.

Figures (5)

• Figure 1: (a) Single and (b) two-boson scattering process.
• Figure 2: Bosonic fluctuation generated due to strong correlation at $n=0.7$. (a)Bosonic spectral function $\rho_{D_{N}}(\omega)$ as a function of $\omega$ and (b) boson frequency(blue) as a function of temperature. Orange and purple line indicate boson frequency associated with $\Sigma_{1}$ and $\Sigma_{2}$ respectively and black line is $\Omega=T$ straight line. The intersection of $\Omega_{1}$ and $\Omega_{2}$ with the $Y=T$ straight line provides two frequency scales respectively.
• Figure 3: Spectral function of strongly correlated electrons. (a)Spectral function at different temperature, as a function of $\omega$. (b)First derivative of spectral function with $\omega$ at different temperatures and (c) different doping concentrations. (d)The variation of quasiparticle weight with doping.
• Figure 4: The dip in the self-energy is due to coherence. Imaginary part of the self-energy is plotted with $\omega$ for (a)$T=0.01$ and (b) $T=0.001$. The contributions of the two distinct processes to the self-energy are plotted separately and at low temperature, contribution from $\Sigma_{2}$ is dominant. The total self-energy for different (c)temperatures and (d) doping is plotted with $\omega$.
• Figure 5: DC resistivity showing linear as well as quadratic $T$ behavior. (a) Resistivity is plotted with temperature showing linear scaling. The contribution from $\Sigma_{2}$ to resistivity show upturn at very low temperature, shown in inset (b). The low temperature behavior is magnified in (b) with blue line indicate spline interpolation of the data. (c) At extreme low temperature, the resistivity data(orange) is fitted with $T^2$(blue) to extract $T_{FL}$. Two linear fits are shown in the inset. (d) The phase-diagram from our numerical simulation.