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Journal of Physics Condensed Matter

Strong antiferromagnetic correlation effects on the momentum distribution function of the Hubbard model

Adolfo Avella, Ferdinando Mancini

Published May 29, 2009• 11 citations
Publisher

Abstract

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).

DOI
10.1088/0953-8984/21/25/254209

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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).
Correlation effects in the one-dimensional Hubbard model are studied by application of the L-resolvent method. The calculations are well beyond one-particle mean field approximation. All correlations involving two neighboring sites are included exactly and higher order correlations are approximated. The effects of varying temperature, band filling, Coulomb repulsion and external magnetic field are investigated. Two-site correlations for non-half-filled band fillings are calculated for the first time. Some exact relations between correlation functions are derived by electron-hole symmetry. Results indicate that short-range spin correlations always favor antiferromagnetic order. Large Coulomb repulsion induces a gap in the excitation spectrum and a metal-insulator transition is predicted as the Coulomb repulsion parameter is changed.
Strong electron correlations lie at the origin of high-temperature superconductivity. Its essence is believed to be captured by the Fermi-Hubbard model of repulsively interacting fermions on a lattice. Here we report on the site-resolved observation of charge and spin correlations in the two-dimensional (2D) Fermi-Hubbard model realized with ultracold atoms. Antiferromagnetic spin correlations are maximal at half-filling and weaken monotonically upon doping. At large doping, nearest-neighbor correlations between singly charged sites are negative, revealing the formation of a correlation hole, the suppressed probability of finding two fermions near each other. As the doping is reduced, the correlations become positive, signaling strong bunching of doublons and holes, in agreement with numerical calculations. The dynamics of the doublon-hole correlations should play an important role for transport in the Fermi-Hubbard model.
Anomalous properties of the normal state of a strongly correlated electron system described by an attractive extended Hubbard model are investigated. The equations of motion of the Green’s functions are calculated with the two-pole approximation which gives rise to quasiparticle renormalized bands. The two-pole approximation leads to a set of correlation functions. In particular, the antiferromagnetic correlation function plays an important role as a source of anomalies in the normal state of the model. The uniform static magnetic susceptibility as a function of occupation n T and temperature is calculated. At low temperatures, the susceptibility presents a peak for n T ≃ 0.80. The results suggest that it is the onset of short-range antiferromagnetic correlations, which could be a mechanism for the pseudogap. The Fermi surface, defined by the spectral function , is presented for different dopings. It has been observed that above n T ≃ 0.80 the ordinary Fermi surface evolves to a hole pocket with pseudogaps near the antinodal points (0,π) and (π,0).
The ground state of the two-dimensional (2D) Hubbard model is investigated by adopting improved wave functions that take into account intersite electron correlation beyond the Gutzwiller ansatz. The ground-state energy is lowered considerably, giving the best estimate of the ground-state energy for the 2D Hubbard model. There is a crossover from weakly to strongly correlated regions as the on-site Coulomb interaction UUU increases. The antiferromagnetic correlation induced by UUU is reduced for hole doping when UUU is large, being greater than the bandwidth, thus increasing the kinetic energy gain. The spin and charge fluctuations are induced in the strongly correlated region. These antiferromagnetic and kinetic charge fluctuations induce electron pairings, which would result in high-temperature superconductivity.
Anomalous properties of the normal state of a strongly correlated electron system described by an attractive extended Hubbard model are investigated. The equations of motion of the Green s functions are calculated with the two-pole approximation which gives rise to quasiparticle renormalized bands. The two-pole approximation leads to a set of correlation functions. In particular, the antiferromagnetic correlation function h~Si · ~Sji plays an important role as a source of anomalies in the normal state of the model. The uniform static magnetic susceptibility as a function of occupation nT and temperature is calculated. At low temperatures, the susceptibility presents a peak for nT ≃ 0.80. The results suggest that it is the onset of short range antiferromagnetic correlations, which could be a mechanism for the pseudogap. The Fermi surface, defined by the spectral function A(ω = 0,~k), is presented for different dopings. It has been observed that above nT ≃ 0.80 the ordinary Fermi surface evolves to a hole-pocket with pseudogaps near the antinodal points (0, π) and (π, 0).
We describe a low-temperature approach to the two-dimensional half-filled Hubbard model which allows us to study both antiferromagnetism and single-particle properties. This approach ignores amplitude fluctuations of the antiferromagnetic (AF) order parameter and is valid below a crossover temperature TX{T}_{X}TX​ which marks the onset of AF short-range order. Directional fluctuations (spin waves) are described by a nonlinear sigma model $(\mathrm{NL}\ensuremath{\sigma}\mathrm{M})$ that we derive from the Hubbard model. The parameters of the $\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$---the spin stiffness and spin-wave velocity---are calculated as a function of the Coulomb repulsion U. The $\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$ is solved by a saddle-point approximation within the CP1{\mathrm{CP}}^{1}CP1 representation where the N\'eel field is parametrized by two Schwinger bosons. At zero temperature, there is always Bose condensation of the Schwinger bosons, which signals AF long-range order for any value of the Coulomb repulsion. At finite temperature, the AF long-range order is suppressed (in agreement with the Mermin-Wagner theorem), but the AF correlation length remains exponentially large. In the CP1{\mathrm{CP}}^{1}CP1 representation, the fermion field is naturally expressed as the product of a Schwinger boson and a pseudofermion whose spin is quantized along the (fluctuating) N\'eel field. This allows us to write the fermion Green's function as the product (in direct space) of the Schwinger boson propagator (which is derived from the $\mathrm{NL}\ensuremath{\sigma}\mathrm{M})$ and the pseudofermion propagator. At zero temperature and weak coupling, our results are typical of a Slater antiferromagnet. The AF gap is exponentially small; there are well-defined Bogoliubov quasiparticles (QP's) (carrying most of the spectral weight) coexisting with a high-energy incoherent excitation background. As U increases, the Slater antiferromagnet progressively becomes a Mott-Heisenberg antiferromagnet. The Bogoliubov bands evolve into Mott-Hubbard bands separated by a large AF gap. A significant fraction of spectral weight is transferred from the Bogoliubov QP's to incoherent excitations. At finite temperature, there is a metal-insulator transition between a pseudogap phase at weak coupling and a Mott-Hubbard insulator at strong coupling. Finally, we point out that our results straightforwardly translate to the half-filled attractive Hubbard model, where the $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$ charge and q=0\mathbf{q}=0q=0 pairing fluctuations combine to form an order parameter with SO(3) symmetry.