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Physical review. B, Condensed matter

Momentum distribution function for the two-dimensionalt-Jmodel

Rajiv R. P. Singh, Rodney L. Glenister

Published Dec 1, 1992• 33 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.46.14313

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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.
The evolution of the Fermi surface upon hole doping is studied in the t-J model of correlated electrons by exact diagonalization of chains and planes. In one dimension at low hole doping, the momentum distribution function n(k) indicates the presence of pocketlike features at the (noninteracting) Fermi momentum, while increasing the density of holes a large Fermi surface is observed. Although the results in two dimensions are consistent with this picture, conclusive evidence for the existence of hole pockets (at intermediate doping levels) cannot be provided in the present study of 4\ifmmode\times\else\texttimes\fi{}4 and \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 square lattices. In order to improve the resolution in momentum space, twisted boundary conditions are used for the two-dimensional clusters.
We have calculated the high temperature expansion for the density correlation function N(q) of the two-dimensional t-J model. On extrapolation by Pad\'e approximants to low temperatures we find that N(q) has 2kFSF{\mathbf{k}}_{\mathit{F}}^{\mathrm{SF}}kFSF​ as a characteristic wave vector. Previous studies have shown that nk{\mathit{n}}_{\mathbf{k}}nk​ has a steplike feature at kF{\mathbf{k}}_{\mathit{F}}kF​ and S(q) has 2kF{\mathbf{k}}_{\mathit{F}}kF​ as a characteristic wave vector. Here kF{\mathit{k}}_{\mathit{F}}kF​ and kFSF{\mathit{k}}_{\mathit{F}}^{\mathrm{SF}}kFSF​ are the Fermi wave vectors of the nearest-neighbor square lattice tight-binding and spinless fermion models, respectively. By comparison to known results for one dimension this suggests spin-charge separation in the two-dimensional t-J model.
Strong antiferromagnetic correlations can radically change the behavior of an otherwise paramagnetic system, inducing anomalous effects in the single particle properties and driving the behavior of spin-spin response functions. In order to investigate such physics, we have studied the momentum distribution function of the two-dimensional Hubbard model at low doping, low temperatures and high values of the on-site Coulomb repulsion. The interpretation of the results has greatly benefited from the parallel analysis of the filling, temperature and interaction dependences of the spin-spin correlation function, the antiferromagnetic correlation length and the pole of the spin-spin propagator. On reducing doping or temperature and on increasing the interaction strength, the correlations become stronger and stronger and the Fermi surface develops hole and electron pockets and shows a dual nature (small-large).
Ground states of the two-dimensional t - t '- J model with one and two holes in 4×4 sites (with periodic boundary conditions) are studied numerically. Using a Lanczos algorithm, we calculate the ground-state energy and momentum distribution, and the phase diagram in the plane of J / t and t '/ t is presented. The momentum distribution for J / t =0.25 is compared with the Fermi surface obtained in the mean-field theory. It is shown that the t '/ t dependences of the momentum distribution are consistent with the mean-field approximation, although there are quantitative differences between them.
The 2D t-J model is studied with exact-diagonalization techniques applied to clusters of sixteen to twenty sites with various hole doping levels. Already for two holes (\ensuremath{\ge}10% doping), a large electronic Fermi surface, compatible with Luttinger's theorem, is observed. The full single-particle Green's function is examined, and is shown to exhibit quasiparticlelike behavior, with dispersion consistent with the band structure of the noninteracting limit, and bandwidth scaling approximately as J for J smaller than t.
The underlying Fermi surface is a key concept for strongly interacting electron models and has been introduced to generalize the usual notion of the Fermi surface to generic (superconducting or insulating) systems. By using improved correlated wave functions that contain backflow and Jastrow terms, we examine the two-dimensional ttt-${t}^{\ensuremath{'}}$ Hubbard model and find a nontrivial renormalization of the topology of the underlying Fermi surface close to the Mott insulator. Moreover, we observe a sharp crossover region, which arises from the metal-insulator transition, from a weakly interacting metal at small coupling to a resonating valence-bond superconductor at intermediate coupling. A violation of the Luttinger theorem is detected at low hole dopings.