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Journal of the Physical Society of Japan

Spin Excitations and Momentum Distribution in the Two-Dimensional Extendedt-JModel

Akiharu Miyanaga, Yasumasa Hasegawa, Hidetoshi Fukuyama

Published Jan 15, 1999• 0 citations

Abstract

The t ′ and t ′′ -dependences of the dynamical spin correlation function S ( q , ω) of the 2D t - t ′ - t ′′ - J model are studied numerically based on the Lanczos algorithm for two holes on 4 ×4 sites. In particular the spin excitations at q =( π, π) ≡ q 0 are examined in detail and compared with results of the mean-field theory. The spin excitations turned out to be drastically different between YBCO( t ′ =-0.17, t ′′ =0.2) and YBCO(II)( t ′ =-0.5, t ′′ =0)-type, although both types reproduce the similar Fermi surfaces of YBCO and have the similar S ( q 0 , ω) in the mean-field theory. Further understanding of the properties of spin excitation for these two choices of t ′ and t ′′ are pursued by calculating the momentum distribution in the excited states. The spin excitations S ( q 0 , ω) for YBCO(II)-type are shown to be of collective type, while those for YBCO appear to be mainly individual.

DOI: 10.1143/jpsj.68.204

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The t ′ and t ′′ -dependences of the dynamical spin correlation function S ( q , ω) of the 2D t - t ′ - t ′′ - J model are studied numerically based on the Lanczos algorithm for two holes on 4 ×4 sites. In particular the spin excitations at q =( π, π) ≡ q 0 are examined in detail and compared with results of the mean-field theory. The spin excitations turned out to be drastically different between YBCO( t ′ =-0.17, t ′′ =0.2) and YBCO(II)( t ′ =-0.5, t ′′ =0)-type, although both types reproduce the similar Fermi surfaces of YBCO and have the similar S ( q 0 , ω) in the mean-field theory. Further understanding of the properties of spin excitation for these two choices of t ′ and t ′′ are pursued by calculating the momentum distribution in the excited states. The spin excitations S ( q 0 , ω) for YBCO(II)-type are shown to be of collective type, while those for YBCO appear to be mainly individual.

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 dynamical spin susceptibility χ( q , ω), of the t-J model in two-dimensional square lattice have been studied based on the mean field approximation to the slave-boson formalism. The static spin susceptibility, χ( q , 0), and Im χ( q , ω) at various energy, ω, have been calculated. We found; 1) χ(0, 0) has only weak temperature dependence 2) T 1 T ∝( T +θ) for

T\gtrsim0.1{J}

with θ linearly dependent on the doping rate, δ 3) T 1 T has a minimum at T =(0.1∼0.2) J 4) Im χ( q , ω) at q = Q ≡(π, π) has a gap like structure as a function of ω if the temperature is low. All these are consistent with experimental results.

The dynamical spin susceptibility χ( q , ω), of the t-J model in two-dimensional square lattice have been studied based on the mean field approximation to the slave-boson formalism. The static spin susceptibility, χ( q , 0), and Im χ( q , ω) at various energy, ω, have been calculated. We found; 1) χ(0, 0) has only weak temperature dependence 2) T 1 T ∝( T +θ) for

T\gtrsim0.1{J}

with θ linearly dependent on the doping rate, δ 3) T 1 T has a minimum at T =(0.1∼0.2) J 4) Im χ( q , ω) at q = Q ≡(π, π) has a gap like structure as a function of ω if the temperature is low. All these are consistent with experimental results.

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We report a calculation of the dynamics of more than one hole in the t-J model using the Lanczos algorithm. The hole spectral weight develops a large quasiparticle peak that describes two holes in the same momentum state on the pseudo-Fermi-surface with antiparallel spins. We also show that doping leads to a narrowing of the bandwidth of the spin-wave dispersion. A larger number of higher-energy subpeaks in the spectral function (compared to half filling) are observed, although they are not predicted by mean-field theory.

The dynamical spin susceptibility χ(q, ω), of the t-J model in two-dimensional square lattice have been studied based on the mean field approximation to the slave-boson formalism. The static spin susceptibility, χ(q, 0), and Im χ(q, ω) at various energy, ω, have been calculated. We found; 1) χ(0, 0) has only weak temperature dependence 2) T1T ∝ (T+θ) for T≳0.1J with θ linearly dependent on the doping rate, δ 3) T1T has a minimum at T= (0.1∼0.2)J 4) Im χ(q, ω) at q = Q = (π, π) has a gap like structure as a function of ω if the temperature is low. All these are consistent with experimental results.