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Journal of Experimental and Theoretical Physics

Spin susceptibilities for the Hubbard model in a band approach

Alexander A. Ovchinnikov, M. Ya. Ovchinnikova

Published Sep 1, 1999• 0 citations
Publisher

Abstract

The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2 D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω ( Q )= c | Q −(π, π)| near Q ∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X ″( Q,ω →0) gives the same mode with a peak at Q ∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X ″( Q,ω →0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector.

DOI
10.1134/1.559016

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The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2 D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω ( Q )= c | Q −(π, π)| near Q ∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X ″( Q,ω →0) gives the same mode with a peak at Q ∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X ″( Q,ω →0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector.
We present a comprehensive study of the 2D one-band Hubbard model applying the spin rotation invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors Q=(π,π),(0,π), and (0,0) we find incommensurate phases where the ordering wave vectors Q=(Q,Q), and (Q,π) vary continuously with filling, interaction strength or temperature. The mean field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the (Q,Q) and (Q,π) phases, indicating a first order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength and temperature. Finally, a temperature-interaction strength phase diagram is established.
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 study spin fluctuations in the spiral phase of the two-dimensional Hubbard model at low doping on the basis of the spin-particle-hole coherent-state path integral. In the strong correlation limit, we obtain an analytical expression of the spin-wave excitations over the entire Brillouin zone except in the vicinity of q=0{\bf q}=0q=0. We discuss the validity of the Hartree-Fock and random-phase approximations in the strong-coupling limit, and compare our results with previous numerical and analytical calculations. Although the spiral phase is unstable, as shown by a negative mean-field compressibility and the presence of imaginary spin-fluctuation modes, we expect the short-wavelength fluctuation modes (with real energies) to survive in the actual ground-state of the system.
Dynamical spin and charge susceptibility and collective modes are studied in the framework of the random phase approximation. They are calculated from the wave function of the selfconsistently obtained ground state, including all possible higher harmonics components of the ordering vector Q . We investigate a spin wave excitation in the spin transverse mode, and phason excitation related to the domain-wall motion in the spin longitudinal and charge modes. We consider the dispersion curve of the collective mode, and discuss the dependence on the on-site U interaction and the period of the incommensurate structure.
We present a comprehensive study of the two-dimensional one-band Hubbard model applying the spin-rotation-invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$, $(0,\ensuremath{\pi})$, and (0,0) we find incommensurate phases where the ordering wave vectors Q=(Q,Q)\mathbf{Q}=(Q,Q)Q=(Q,Q) and $(Q,\ensuremath{\pi})$ vary continuously with filling, interaction strength, or temperature. The mean-field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the (Q,Q)(Q,Q)(Q,Q) and $(Q,\ensuremath{\pi})$ phases, indicating a first-order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength, and temperature. Finally, a temperature-interaction strength phase diagram is established.
We have calculated the elementary-spin-excitation spectrum of undoped and doped Hubbard models in one and two dimensions. We have obtained the gap of the spectrum at Q=(\ensuremath{\pi},\ensuremath{\pi}) in the doped strong-coupling Hubbard model by a Lanczos diagonalization study of the \ensuremath{\surd}10 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}10 site cluster. The result is qualitatively in agreement with the experimental observation of the ``spin gap'' by Rossat-Mignod et al. We conclude that the ``spin gap'' can be accounted for with the doped strong-coupling Hubbard model without any symmetry reductions and is one of the intrinsic properties of the Hubbard model.