Universal quasi-Fermi liquid physics of one-dimensional interacting fermions

Abstract

We present a class of one-dimensional generic spinless fermion lattice Hamiltonians that express quasi-Fermi liquid physics, manifesting both Luttinger and Fermi liquid features due to solely irrelevant interactions. Using infinite matrix product state techniques, we unveil its universal structure by calculating static and dynamic responses. Key features include a finite discontinuity in the momentum distribution at the Fermi level, despite power-law singularities in the spectral function protected by particle-hole symmetry. Away from half-filling Landau quasiparticles emerge. Charge dynamics show either high-energy bound states or concentration of spectral weight within the continuum for attractive or repulsive interactions, respectively. These universal features are realized across multiple models and energy scales thus reifying the quasi-Fermi liquid as a unique paradigm for one-dimensional fermions.

Figures (4)

• Figure 1: Normalized spectral functions for four qFL models and their densities ($\chi=104$ with full excitation spectrum): (a) $VV_2$, $n = 0.5$; (b) $Vt'_c$, $n = 0.41$; (c) $Vt_c$, $n = 0.25$; (d) $V_2t_c$, $n = 0.26$. The horizontal line indicates the Fermi level. Notice the particle-hole symmetry for the $VV_2$ model relative to the asymmetry of the others.
• Figure 2: FES scaling exponents as a function of momentum for the qFL models shown in Fig. \ref{['fig:Ak']}. $\eta_{\max} = 1~(\eta_{\max} < 1)$ corresponds to quasiparticle (power-law) excitations.
• Figure 3: Normalized dynamic structure factor for four qFL models ($\chi=104$ with full excitation spectrum): (a) $VV_2$, (b) $Vt'_c$, (c) $Vt_c$, (d) $V_2t_c$. There are two branches at half-filling (a) and three otherwise (b)-(d). Note the dominant upper branch in (a),(c),(d) above a faint continuum [see Figs. \ref{['fig:etaq']}(a) and \ref{['fig:etaq']}(b)], mimicking the attractive-$tV$ model, suggesting bound states. Next, note the dominant middle branch in (b) along with faint upper/lower branches, mimicking the repulsive-$tV$ model. Strengthening the comparison, we plot the free-fermion dispersion (white), using a bandwidth $J_{\rm eff}$ calculated from $A(k,\omega)$, and the ferromagnetic-XXZ magnon dispersion (orange); $J_{\rm bound}$ is fit to the energy scale. The discrete lines will fuse into a smooth continuum as $\chi \to \infty$.
• Figure 4: FES scaling exponents, $\eta_{\max}$, and half width at half maximum, $\Sigma_\pm$, as a function of momentum (right column) of the peaks in the momentum cuts (left column) for the three attractive-qFL models. For (a) and (b), as $q \rightarrow \pi$ the lineshape evolves toward a Lorentzian-like peak ($\Sigma \rightarrow 1$). In (c) we have a similar behavior instead near $q=0.6\pi$. Given effective attractive interactions, this peak represents an exciton hybridized with the surrounding excitations causing $\eta_{\rm max} < 1$.