Pseudogapped Fermi liquids from emergent quasiparticles

Abstract

We propose an interacting model that is exactly solvable in any spatial dimension and gives rise to a Fermi liquid (FL) featuring a pseudogapped (PG) single-particle spectral function and a vanishing quasiparticle (QP) weight at half-filling, without invoking Mott physics. The PG originates from a purely fermionic mechanism through emergent QPs arising from a correlated hopping interaction. By employing an appropriate coherent-state basis, we derive a Gaussian path-integral representation of the partition function, which enables systematic treatments of deviations from the Gaussian limit using standard many-body techniques, such as diagrammatic perturbation theory or mean-field theory. We explicitly demonstrate and discuss several properties of the exactly solvable limit on the square lattice, including the mechanism for temperature-dependent PG opening, the singular behavior of the self-energy, the violation of the Luttinger sum rule, and the role of Luttinger and Fermi surfaces. Finally, we explore quantum phase transitions between PG-FLs and Landau FLs.

Figures (10)

• Figure 1: Single-particle properties on the square lattice with $t = 0.5$ and $t' = -0.15 t$ [cf. Eq. \ref{['eq:t_tp_dispersion']}] at half-filling: (a) $T=0$${\mathbf{k}}$-resolved spectral function [$\Gamma = (0,0)$, $X = (0,\pi)$, $\Pi = (\pi,\pi)$], (b) corresponding self-energy (LS: Luttinger surface), (c) $T$-dependent electronic occupation number and (d) local spectral function. We used periodic boundary conditions with $L_x \times L_y = 1024 \times 1024$.
• Figure 2: (a) Average phase shift $v_{\delta}$ [c.f. Eq. \ref{['eq:Luttinger_sum_rule']}] and Luttinger integral $I_L$ versus filling, for a square lattice with $t = 0.5$ and $t' = -0.15 t$. (b) Real parts of $G_{{\mathbf{k}}\sigma}(\mathrm{i} 0^{+})$ for selected fillings marked in (a), illustrating the location of Luttinger surfaces (LS, white) and Fermi surfaces (FS, abrupt blue to red boundary).
• Figure 3: (a) Spectral function of an impurity model with hybridization $V_x$ for both $q$ and $c$ [c.f. Eq. \ref{['eq:Himp']}]. (b) Local spectral function from a GDMFT solution on the $d \to \infty$ Bethe lattice. The GDMFT has been initialized with a PG-FL solution. (c) Entropy of an $L=8$ 1d chain.
• Figure 4: (a) ${\mathbf{k}}$-resolved spectral function [$\Gamma = (0,0)$, $X = (0,\pi)$, $\Pi = (\pi,\pi)$], (b) corresponding self-energy, (c) ${\mathbf{k}}$-resolved QP spectral function, and (d) QP DOS and $q$-particle DOS for the $t$-$t'$ square lattice model discussed in the main text, at filling $n_{\sigma} = 0.6$. For better visualization, we applied Lorentzian broadening of width $\eta = 5\times 10^{-3}$ in (a-c). To obtain the data in panel (d), we regularized the integrals in Eqs. \ref{['eq:Aast_loc']} and \ref{['eq:Aq_loc']} with Lorentzian broadening of width $\eta = 10^{-3}$.
• Figure 5: (a) ${\mathbf{k}}$-resolved QP spectral function corresponding to the spectral function and self-energy shown in Fig. \ref{['fig:Hq_ttp_square']}(a,b), and (b) corresponding QP and $q$-particle DOS. We applied Lorentzian broadening of width $\eta = 5\times 10^{-3}$ in (a) for better visualization, and of width $\eta = 10^{-3}$ in (b) to regularize the integrals in Eqs. \ref{['eq:Aast_loc']} and \ref{['eq:Aq_loc']}.