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arXiv:cond-mat/9803140 · Physical Review Letters

Violation of Luttinger's Theorem in the Two-Dimensional t - J Model

W. O. Putikka, Marco U. Luchini, Rajiv R. P. Singh

Published Oct 5, 1998• 58 citations
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Abstract

We have calculated the high temperature series for the momentum distribution function ${n}_{\mathbf{k}}$ of the 2D $t\ensuremath{-}J$ model to twelfth order in inverse temperature. By extrapolating the series to $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.2J$ we searched for a Fermi surface of the 2D $t\ensuremath{-}J$ model. We find that three criteria used for estimating the location of a Fermi surface violate Luttinger's theorem, implying that the $t\ensuremath{-}J$ model does not have an adiabatic connection to a noninteracting model.

DOI
10.1103/physrevlett.81.2966

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We study the momentum distribution function n(k) for the two-dimensional t-J model by high-temperature expansions. Starting with a k-independent n(k) at T=\ensuremath{\infty}, we observe the buildup of a sharp Fermi-surface-like feature as the temperature is lowered. For very small density of electrons, our results are clearly consistent with Luttinger's theorem. At all fillings the contours of constant n(k) closely resemble those of the tight-binding model. No evidence for pocketlike Fermi surfaces is seen. Far from the Fermi surface n(k) has a particle-hole asymmetry similar to that found in the one-dimensional, U=\ensuremath{\infty} Hubbard model.
One of the fundamental questions about high-temperature cuprate superconductors is the size of the Fermi surface underlying the superconducting state. By analyzing the single-particle spectral function for the Fermi-Hubbard model as a function of repulsion UUU and chemical potential $\ensuremath{\mu}$, we find that the Fermi surface in the normal state undergoes a transition from a large Fermi surface matching the Luttinger volume as expected in a Fermi liquid, to a Fermi surface that encloses fewer electrons that we dub the ``Luttinger breaking'' phase, as the Mott insulator is approached. This transition into a non-Fermi-liquid phase that violates the Luttinger count occurs at a critical density in the absence of any other broken symmetry. We obtain the Fermi-surface contour from the spectral weight ${A}_{\mathbf{k}}(\ensuremath{\omega}=0)$ and from an analysis of the singularities of the Green's function ReGk(E=0)\mathrm{Re}\phantom{\rule{0.16em}{0ex}}{G}_{\mathbf{k}}(E=0)ReGk​(E=0), calculated using determinantal quantum Monte Carlo and analytic continuation methods. We discuss our numerical results in connection with experiments on Hall measurements, scanning tunneling spectroscopy, and angle-resolved photoemission spectroscopy.
Breakdown of Landau's hypothesis of adiabatic continuation from noninteracting to fully interacting electrons is commonly believed to bring about a violation of Luttinger's theorem. Here, we elucidate what may go wrong in the proof of Luttinger's theorem. The analysis provides a simple way to correct Luttinger's expression of the electron number in single-band models where perturbation theory breaks down through the birth of a Luttinger surface without symmetry breaking. In those cases, we find that the Fermi volume only accounts for the doping away from half-filling. In the hypothetical circumstance of a non-symmetry-breaking Mott insulator with a Luttinger surface, our analysis predicts the noteworthy existence of quasiparticles whose Fermi surface is just the Luttinger one. Therefore, those quasiparticles can be legitimately regarded as spinons, and the Mott insulator with a Luttinger surface as realization of a spin-liquid insulator.
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