We study the finite-energy density phase diagram of spinless fermions with attractive interactions in one dimension in the presence of uncorrelated diagonal disorder. Unlike the case of repulsive interactions, a delocalized Luttinger-liquid phase persists at weak disorder in the ground state, which is a well-known result. We revisit the ground-state phase diagram and show that the recently introduced occupation-spectrum discontinuity computed from the eigenspectrum of the one-particle density matrix is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization group scheme to study the finite-size dependence of the conductance, which also resolves the existence of the Luttinger liquid and is computationally cheap. Our main results concern the finite-energy density case. Using exact diagonalization and by computing various established measures of the many-body localization-delocalization transition, we argue that the zero-temperature Luttinger liquid smoothly evolves into a finite-energy density ergodic phase without any intermediate phase transition.
We used exact diagonalization of small clusters and exact results in various limits to determine the phase diagram and the critical exponents of the one-dimensional (1D) U-V model at quarter-filling. We found an instability of the Luttinger liquid to a charge density wave (CDW) insulator across a boundary going from ( U, V ) = (+ ∞ , 2 t ) to (4 t , + ∞ ). In the metallic phase, the dominant fluctuations are superconducting if V is large enough and spin density wave (SDW) otherwise. In the latter case, the critical exponent α of the momentum distribution does not exceed 9/16. The relevance of these results to 1D organic conductors is discussed.
We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in the rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.
We investigate the indirect interaction between two isolated impurities in a Luttinger liquid described by a microscopic lattice model. To treat the electron-electron interaction
U, the functional renormalization group method is used. For comparison, we also study the
U=0 case. We find that for a wide range of impurity parameters the impurity interaction
V12 as a function of their separation
r oscillates with decaying amplitude between being attractive and repulsive. For half-filling of the band and in a crossover regime between weak and strong impurities, the interaction becomes purely attractive. For
U=0 and independent of the impurity strength, the amplitude of the interaction energy falls off as
1∕r. For
U>0, the decay for small separations and weak to intermediate impurities is governed by a
U dependent exponent larger than $\ensuremath{-}1$, which crosses over to $\ensuremath{-}1$ for large
r. The crossover scale depends on the impurity strength and
U. We present simple pictures which explain our results in the limits of weak and strong impurities. We finally also consider attractive interactions
U<0.
We study the interplay between an on-site Hubbard repulsion and quasiperiodic potential in one-dimensional fermion chains using the density matrix renormalization group. We find that, at half filling, the quasiperiodic potential can destroy the Mott gap, leading to a metallic Luttinger liquid phase between the gapped Mott insulator at strong repulsion and the localized gapless Aubry-Andr\'e insulator at strong quasiperiodic potential. Away from half filling, the metallic phase of the interacting model persists to larger critical strengths of the potential than in the noninteracting case, suggesting interaction-stabilized delocalization at finite doping. We characterize the Luttinger liquid through its charge and spin correlations, structure factors, and entanglement entropy.