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Physical review. B, Condensed matter

Crossover from Fermi liquid to Luttinger-liquid-like behavior in the two-dimensional Hubbard model

D. N. Aristov, S. V. Maleyev, A. G. Yashenkin

Published Aug 1, 1993• 10 citations
Publisher

Abstract

The crossover from conventional Fermi-liquid (FL) behavior to the Luttinger-liquid-like behavior in the two-dimensional single-band small-U Hubbard model near half filling is demonstrated. The applicability of the FL picture is discussed. This crossover is reproduced in the fermionic channel of the t-J model, if the fermion-fermion interaction is taken into account. The results are in qualitative agreement with the normal-state resistivity and photoemission data on the high-${\mathit{T}}_{\mathit{c}}$ cuprates.

DOI
10.1103/physrevb.48.3527

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The crossover from conventional Fermi-liquid (FL) behavior to the Luttinger-liquid-like behavior in the two-dimensional single-band small-U Hubbard model near half filling is demonstrated. The applicability of the FL picture is discussed. This crossover is reproduced in the fermionic channel of the t-J model, if the fermion-fermion interaction is taken into account. The results are in qualitative agreement with the normal-state resistivity and photoemission data on the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates.
Analysis of interacting fermion systems shows that there are two fundamentally different fixed points, Fermi-liquid theory and ``Luttinger-liquid theory'' (Haldane), a state in which charge and spin acquire distinct spectra and correlations have unusual exponents. The Luttinger liquids include most interacting one-dimensional systems, and some higher- (especially two) dimensional systems in which the band spectrum is bounded above, systems with Mott-Hubbard gaps and an upper Hubbard band. We give a theory which is useful in calculating normal-state, and some superconducting, properties of high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors.
We study the Kohn-Luttinger effect in a two-dimensional (2D) nested fermion liquid with a repulsive interaction via the renormalization group method and identify the resulting order parameter symmetry. Using the band structure of the 2D Hubbard model close to half-filling as a prototype, we construct an effective low-energy theory. We use multidimensional bosonization to incorporate the zero-sound channel and find marginal Fermi liquid behavior in the absence of any instability. We show an analog of the Landau theorem in nested fermion liquids, which serves as the criterion of the BCS instability. Including repulsive or antiferromagnetic exchange interactions in the low-energy theory, we show that the ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$-wave BCS channel is renormalized to be the most attractive. Below half-filling, when the nesting is not perfect, there is competition between the spin-density-wave (SDW) and the BCS channels; when the SDW coupling is small enough, there occurs a ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$-wave superconducting instability at sufficiently low temperatures.
We discuss spectra calculated for the two-dimensional Hubbard model in the intermediate coupling regime with the dynamical cluster approximation, which is a nonperturbative approach. We find a crossover from a normal Fermi liquid with a Fermi surface closed around the Brillouin-zone center at large doping to a non-Fermi liquid for small doping where the Fermi surface is holelike, closed around $M=(\ensuremath{\pi},\ensuremath{\pi}).$ The topology of the Fermi surface at low doping indicates a violation of Luttinger's theorem. We discuss different ways of presenting the spectral data to extract information about the Fermi surface. A comparison to recent experiments is presented.
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We analyze the low energy behavior of interacting fermions in continuous dimensions d between one and two. It is shown that Fermi liquid fixed points are stable with respect to residual scattering of quasiparticles by regular interactions in any dimension above one, while the structure of corrections to quasiparticle behavior changes drastically below two dimensions. The crossover from Luttinger liquid behavior in 1D to Fermi liquid behavior in higher dimensions is described by a tomographic Luttinger model with effective interactions approaching zero with a power d-1 of the distance from the Fermi surface.
Fermi surface reconstruction in cuprates can lead to an abrupt change in the Fermi momentum kF{k}_{F}kF​ between different phases. This phenomenon remains a subject of debate and is at the heart of an ongoing discussion about the nature of the metallic state in the pseudogap regime. Here we study a minimal model of a kF{k}_{F}kF​ changing crossover in the one-dimensional Fermi-Hubbard model, where a tuning of the on-site interaction leads to a crossover between a spin-1/21/21/2 Luttinger liquid with small Fermi momentum and a spinless chargon liquid with large Fermi momentum. We attribute this to an emergent U(1)U(1)U(1) symmetry in the strongly correlated limit, which can be used to derive a modified Luttinger sum rule recovering the large Fermi momentum. We analyze Friedel oscillations at the edge of a system to directly probe the change of Fermi momentum at zero and nonzero temperature. This paves the way for a direct experimental observation of changes of the Fermi momentum using ultracold fermions in a quantum gas microscope, with possible extensions to higher dimensional systems.