Physical review. B, Condensed matter

Two-loop scattering amplitudes for the finite-charge infinite-UHubbard model: Existence of a spin-exchange collective mode

J. W. Rasul

Published Jul 15, 1994• 4 citations

Abstract

We study the spin-exchange scattering amplitude at two-loop (1/${\mathit{N}}^{2}$) order for the infinite-U Hubbard model away from the metal-insulator filling, with finite electron charge, for which a well-defined 1/N expansion is possible, the mean-field level being equivalent to Gutzwiller enhanced quasiparticles. We find a positive spin-exchange Landau parameter which suggests that the spin-density fluctuations show a well-defined collective mode near the metal-insulator filling. This behavior is interpreted as paralleling the spin and charge separation in the Luttinger liquid.

DOI: 10.1103/physrevb.50.2133

Related papers

Two-loop scattering amplitudes for thet-Jmodel: Evidence for a spin-exchange collective mode

J. W. Rasul

Physical review. B, Condensed matterJan 15, 19951 citation

Resonant zero-sound exchange in the 1/Nexpansion of the infinite-UHubbard model

J. W. Rasul, WENJIE HUANG

Physical review. B, Condensed matterMay 1, 19914 citations

Quasiparticle interactions in the infinite U Hubbard model.

Wei-neng Huang

Jan 1, 19920 citations

Non-Fermi liquids in the two-band extended Hubbard model

J. L Smith, Qimiao Si A

Europhysics Letters (EPL)Jan 15, 199974 citations

Dynamical t/U Expansion of the Doped Hubbard Model

Wenxin Ding, Rong Yu

arXiv:1906.12071Chinese Physics LettersFeb 28, 20241 citation

The metal-insulator transition in one dimension

Heinz J. Schulz

arXiv:cond-mat/9412036Dec 7, 19947 citations

Physical review. B, Condensed matter

Two-loop scattering amplitudes for the finite-charge infinite-UHubbard model: Existence of a spin-exchange collective mode

J. W. Rasul

Published Jul 15, 1994• 4 citations

Publisher

Abstract

We study the spin-exchange scattering amplitude at two-loop (1/

{\mathit{N}}^{2}

) order for the infinite-U Hubbard model away from the metal-insulator filling, with finite electron charge, for which a well-defined 1/N expansion is possible, the mean-field level being equivalent to Gutzwiller enhanced quasiparticles. We find a positive spin-exchange Landau parameter which suggests that the spin-density fluctuations show a well-defined collective mode near the metal-insulator filling. This behavior is interpreted as paralleling the spin and charge separation in the Luttinger liquid.

DOI: 10.1103/physrevb.50.2133

Related papers

Two-loop scattering amplitudes for thet-Jmodel: Evidence for a spin-exchange collective mode

J. W. Rasul

We study contributions to the spin-exchange scattering amplitude at two-loop (1/ ${\mathit{N}}^{2}$ ) order for the metallic phase of the two-dimensional t-J model, for which a well-defined 1/N expansion is possible. We find for small hole dopings and small exchange couplings (t\ensuremath{\gg}J) a positive spin-exchange Landau parameter, which suggests that the spin-density fluctuations show a well-defined collective mode near the metal-insulator filling. This behavior results from the fact that the chirality fluctuations decouple from and are suppressed relative to the charge fluctuations for large mass enhancements. The result is interpreted as paralleling the collective spin and charge modes characteristic of the Luttinger liquid for low wave vectors.We study contributions to the spin-exchange scattering amplitude at two-loop (1/${\mathit{N}}^{2}$) order for the metallic phase of the two-dimensional t-J model, for which a well-defined 1/N expansion is possible. We find for small hole dopings and small exchange couplings (t\ensuremath{\gg}J) a positive spin-exchange Landau parameter, which suggests that the spin-density fluctuations show a well-defined collective mode near the metal-insulator filling. This behavior results from the fact that the chirality fluctuations decouple from and are suppressed relative to the charge fluctuations for large mass enhancements. The result is interpreted as paralleling the collective spin and charge modes characteristic of the Luttinger liquid for low wave vectors.

Physical review. B, Condensed matterJan 15, 19951 citation

Resonant zero-sound exchange in the 1/Nexpansion of the infinite-UHubbard model

J. W. Rasul, WENJIE HUANG

We study the infinite-U Hubbard model away from half-filling within the 1/N expansion. At order 1/ ${\mathit{N}}^{2}$ we find a substantial contribution to the Cooper-pair scattering amplitude arising from the resonant exchange of two zero-sound modes. This contribution is repulsive and can be identified with strong ferromagnetic spin fluctuations.We study the infinite-U Hubbard model away from half-filling within the 1/N expansion. At order 1/${\mathit{N}}^{2}$ we find a substantial contribution to the Cooper-pair scattering amplitude arising from the resonant exchange of two zero-sound modes. This contribution is repulsive and can be identified with strong ferromagnetic spin fluctuations.

Physical review. B, Condensed matterMay 1, 19914 citations

Quasiparticle interactions in the infinite U Hubbard model.

Wei-neng Huang

The auxiliary boson method and 1/N expansion are applied to the solution of the Hubbard model in the U = $\infty$ limit, in functional integral form. The zero order term in the expansion gives the mean-field result of non-interacting enhanced mass quasiparticles, and the next order gives Gaussian fluctuations around the mean-field value, representing effective interactions between the quasiparticles. From the density-density correlation function, the collective mode indicates a very different behavior away from and close to half filling. The superconducting instability is examined to 1/$N\sp2$ order from the dominant double collective mode exchange. For a parabolic band, there is a p-wave triplet instability. But for a 2D square lattice, there is no superconducting pairing to this order. The effects of disorder on this system are also investigated. For moderate filling, the specific heat and scattering rate have the same results as predicted in the weakly interacting theories. Close to half-filling, the specific heat and scattering rate show a much sharper temperature and energy dependence.The auxiliary boson method and 1/N expansion are applied to the solution of the Hubbard model in the U = $\infty$ limit, in functional integral form. The zero order term in the expansion gives the mean-field result of non-interacting enhanced mass quasiparticles, and the next order gives Gaussian fluctuations around the mean-field value, representing effective interactions between the quasiparticles. From the density-density correlation function, the collective mode indicates a very different behavior away from and close to half filling. The superconducting instability is examined to 1/$N\sp2$ order from the dominant double collective mode exchange. For a parabolic band, there is a p-wave triplet instability. But for a 2D square lattice, there is no superconducting pairing to this order. The effects of disorder on this system are also investigated. For moderate filling, the specific heat and scattering rate have the same results as predicted in the weakly interacting theories. Close to half-filling, the specific heat and scattering rate show a much sharper temperature and energy dependence.

Jan 1, 19920 citations

Non-Fermi liquids in the two-band extended Hubbard model

J. L Smith, Qimiao Si A

We study the non-Fermi liquid behavior in a two-band extended Hubbard model. In the limit of infinite dimensions, where only local correlations are taken into account, this model in the mixed-valence regime is known to display a metallic non-Fermi liquid phase with spin-charge separation. Here we address the effect of intersite RKKY-like interactions using an extended dynamical mean-field approach. We find that the spin-charge separation survives the quantum fluctuations associated with the intersite density-density and spin-exchange interactions. We determine the spin, charge, and single-particle correlation functions in the non-Fermi liquid state.We study the non-Fermi liquid behavior in a two-band extended Hubbard model. In the limit of infinite dimensions, where only local correlations are taken into account, this model in the mixed-valence regime is known to display a metallic non-Fermi liquid phase with spin-charge separation. Here we address the effect of intersite RKKY-like interactions using an extended dynamical mean-field approach. We find that the spin-charge separation survives the quantum fluctuations associated with the intersite density-density and spin-exchange interactions. We determine the spin, charge, and single-particle correlation functions in the non-Fermi liquid state.

Europhysics Letters (EPL)Jan 15, 199974 citations

Dynamical t/U Expansion of the Doped Hubbard Model

Wenxin Ding, Rong Yu

We construct a new U(1) slave-spin representation for the single-band Hubbard model in the large-U limit. The mean-field theory in this representation is more amenable to describe both the spin-charge-separation physics of the Mott insulator at half-filling and the strange metal behavior at finite doping. By employing a dynamical Green’s function theory for slave spins, we calculate the single-particle spectral function of electrons. The result is comparable to that in dynamical mean field theories. We then formulate a dynamical t/U expansion for the doped Hubbard model that reproduces the mean-field results at the lowest order of expansion. To the next order of expansion, it naturally yields an effective low-energy theory of a t–J model for spinons self-consistently coupled to an XXZ model for the slave spins. We show that the superexchange J is renormalized by doping, in agreement with the Gutzwiller approximation. Surprisingly, we find a new ferromagnetic channel of exchange interactions which survives in the infinite U limit, as a manifestation of the Nagaoka ferromagnetism.We construct a new U(1) slave-spin representation for the single-band Hubbard model in the large-U limit. The mean-field theory in this representation is more amenable to describe both the spin-charge-separation physics of the Mott insulator at half-filling and the strange metal behavior at finite doping. By employing a dynamical Green’s function theory for slave spins, we calculate the single-particle spectral function of electrons. The result is comparable to that in dynamical mean field theories. We then formulate a dynamical t/U expansion for the doped Hubbard model that reproduces the mean-field results at the lowest order of expansion. To the next order of expansion, it naturally yields an effective low-energy theory of a t–J model for spinons self-consistently coupled to an XXZ model for the slave spins. We show that the superexchange J is renormalized by doping, in agreement with the Gutzwiller approximation. Surprisingly, we find a new ferromagnetic channel of exchange interactions which survives in the infinite U limit, as a manifestation of the Nagaoka ferromagnetism.

arXiv:1906.12071Chinese Physics LettersFeb 28, 20241 citation

The metal-insulator transition in one dimension

Heinz J. Schulz

The low--energy excited states of a system of interacting one--dimensional fermions in a conducting state are collective charge and spin density oscillations. The unusual physical properties of such a system (called ``Luttinger liquid'') are characterized by the velocities $u_ρ$ and $u_σ$ of the charge and spin excitations, as well as by a parameter $K_ρ$ that determines the power law behavior of correlation functions. Umklapp scattering occuring at half--filling or other commensurate bandfilling can lead to a transition into an insulating state, characterized in particular by a gap in the charge excitations (the Mott--Hubbard gap). The properties in the vicinity of the transition are shown to depend on both the way the transition is approached (constant bandfilling and varying interaction, or constant interaction and varying bandfilling) and on the ``order'' of the commensurability. In particular, even and odd fractional fillings show quite different behavior. This behavior is illustrated in detail using lattice models like the Hubbard model and its extensions.The low--energy excited states of a system of interacting one--dimensional fermions in a conducting state are collective charge and spin density oscillations. The unusual physical properties of such a system (called ``Luttinger liquid'') are characterized by the velocities $u_ρ$ and $u_σ$ of the charge and spin excitations, as well as by a parameter $K_ρ$ that determines the power law behavior of correlation functions. Umklapp scattering occuring at half--filling or other commensurate bandfilling can lead to a transition into an insulating state, characterized in particular by a gap in the charge excitations (the Mott--Hubbard gap). The properties in the vicinity of the transition are shown to depend on both the way the transition is approached (constant bandfilling and varying interaction, or constant interaction and varying bandfilling) and on the ``order'' of the commensurability. In particular, even and odd fractional fillings show quite different behavior. This behavior is illustrated in detail using lattice models like the Hubbard model and its extensions.

arXiv:cond-mat/9412036Dec 7, 19947 citations

We study the spin-exchange scattering amplitude at two-loop (1/

{\mathit{N}}^{2}

We study contributions to the spin-exchange scattering amplitude at two-loop (1/

{\mathit{N}}^{2}

) order for the metallic phase of the two-dimensional t-J model, for which a well-defined 1/N expansion is possible. We find for small hole dopings and small exchange couplings (t\ensuremath{\gg}J) a positive spin-exchange Landau parameter, which suggests that the spin-density fluctuations show a well-defined collective mode near the metal-insulator filling. This behavior results from the fact that the chirality fluctuations decouple from and are suppressed relative to the charge fluctuations for large mass enhancements. The result is interpreted as paralleling the collective spin and charge modes characteristic of the Luttinger liquid for low wave vectors.

We study the infinite-U Hubbard model away from half-filling within the 1/N expansion. At order 1/

{\mathit{N}}^{2}

we find a substantial contribution to the Cooper-pair scattering amplitude arising from the resonant exchange of two zero-sound modes. This contribution is repulsive and can be identified with strong ferromagnetic spin fluctuations.

The auxiliary boson method and 1/N expansion are applied to the solution of the Hubbard model in the U =

\infty

limit, in functional integral form. The zero order term in the expansion gives the mean-field result of non-interacting enhanced mass quasiparticles, and the next order gives Gaussian fluctuations around the mean-field value, representing effective interactions between the quasiparticles. From the density-density correlation function, the collective mode indicates a very different behavior away from and close to half filling. The superconducting instability is examined to 1/$N\sp2$ order from the dominant double collective mode exchange. For a parabolic band, there is a p-wave triplet instability. But for a 2D square lattice, there is no superconducting pairing to this order. The effects of disorder on this system are also investigated. For moderate filling, the specific heat and scattering rate have the same results as predicted in the weakly interacting theories. Close to half-filling, the specific heat and scattering rate show a much sharper temperature and energy dependence.

u_ρ

and

u_σ

of the charge and spin excitations, as well as by a parameter

K_ρ

that determines the power law behavior of correlation functions. Umklapp scattering occuring at half--filling or other commensurate bandfilling can lead to a transition into an insulating state, characterized in particular by a gap in the charge excitations (the Mott--Hubbard gap). The properties in the vicinity of the transition are shown to depend on both the way the transition is approached (constant bandfilling and varying interaction, or constant interaction and varying bandfilling) and on the ``order'' of the commensurability. In particular, even and odd fractional fillings show quite different behavior. This behavior is illustrated in detail using lattice models like the Hubbard model and its extensions.