Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9608053 · Physical review. B, Condensed matter

Statics and dynamics of charge fluctuations in thet-Jmodel

R. Zeyher, Miodrag L. Kulić

Published Oct 1, 1996• 32 citations
arXivHTMLPDF

Abstract

The equation for the charge vertex \ensuremath{\gamma} of the t-J model is derived and solved in leading order of a 1/N expansion, working directly in terms of Hubbard operators. Various quantities which depend crucially on \ensuremath{\gamma} are then calculated, such as the lifetime and the transport lifetime of electrons due to a charge coupling to other degrees of freedom and the charge-charge correlation function. Our results show that the static screening of charges and the dynamics of charge fluctuations depend only weakly on J and are mainly determined by the constraint of having no double occupancies of sites. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.8985

Related papers

Representation of thet-Jmodel using decoupled spin and charge variables

Jan Loos

Using the mapping of the single-occupation space of the t-J model onto the tensor-product space of local spin-1/2 and holon states, the Hubbard operators and their products corresponding to physical quantities are expressed in terms of local spin and holon operators. All relevant operator relations of the t-J model are reproduced by this representation and no projection procedure is needed to remove the redundant degrees of freedom originating from the spin and charge decoupling. It is shown that the time-reversal symmetry requirement makes the essential restriction on the choice of the fictitious spin state associated with the electron-vacancy state in the mapping. The results are critically compared with the treatment of this topic in the paper of Wang and Rice [Phys. Rev. B 49, 4360 (1994)]. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•May 15, 1996•6 citations

Spin-charge separation in thet-Jmodel: Magnetic and transport anomalies

Zheng-Yu Weng, D. N. Sheng, C. S. Ting

A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a ${\mathit{T}}^{2}$ Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-${\mathit{T}}_{\mathit{c}}$ cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.

arXiv:cond-mat/9502113•Physical review. B, Condensed matter•Jul 1, 1995•35 citations

Charge dynamics in strongly-correlated electronic systems

Nguen Dan Tung, Nikolay M. Plakida

We consider the dynamic charge susceptibility and the charge density waves in strongly-correlated electronic systems within the two-dimensional t-J-V model. Using the equation of motion method for the relaxation functions in terms of the Hubbard operators, we calculate the static susceptibility and the spectrum of charge fluctuations as functions of doped hole concentrations and temperature. Charge density waves emerge for a sufficiently strong intersite Coulomb interaction. Calculation of the dynamic charge susceptibility reveals a strong damping of charge density waves for a small hole doping and propagating high-energy charge excitations at large doping.

International Journal of Modern Physics B•Nov 14, 2018•1 citation

Charge dynamics and optical conductivity of the t−J model

George Jackeli, Nikolay M. Plakida

The dynamic charge susceptibility and the optical conductivity are calculated in the planar $t\ensuremath{-}J$ model within the memory function method, working directly in terms of Hubbard operators. The density fluctuation spectrum consists of a damped soundlike mode for small wave vectors and a broad high energy peak $(\ensuremath{\sim}t)$ for large momenta. The study of the optical conductivity shows that electron scattering from spin fluctuations leads to the Drude-frequency dependent relaxation rate which exhibits a crossover from ${\ensuremath{\omega}}^{3/2}$ behavior at low frequencies $(\ensuremath{\omega}<2|\ensuremath{\mu}|),$ to a linear $\ensuremath{\omega}$ dependence for frequencies larger than $2|\ensuremath{\mu}|.$ Due to the spin-polaron nature of charge carriers, extra absorptions arise starting at a frequency $\ensuremath{\omega}\ensuremath{\gtrsim}J.$ The obtained results are in a good agreement with exact diagonalization studies.

arXiv:cond-mat/9810327•Physical review. B, Condensed matter•Aug 15, 1999•23 citations

Perturbation formalism of an exact representation for thet-Jmodel

Zhe Chang

We show an exact representation of the t-J model by making use of a general Holstein-Primakoff transformation. The single occupancy constraint on the electrons is imposed strictly at every lattice site and the t-J Hamiltonian is transformed into an equivalent interacting boson and fermion system. The lowest-order approximation of a systematic perturbative expansion of the representation is shown to correspond to the mean-field theory of the Schwinger-boson approach. The second-order approximation gives the magnon-magnon, magnon-hole, and hole-hole interactions and the high-order antiferromagnetic spin polaron. In particular the second-order approximation takes further account of the renormalization of the magnon frequency and the antiferromagnetic spin polaron. The spectra of holes and magnons are calculated with the Green's function. The relevance of the obtained results to high-${\mathit{T}}_{\mathit{c}}$ superconductors is discussed. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Jan 15, 1996•9 citations

Influence of spin fluctuations on the superconducting transition temperature and resistivity in thet-Jmodel at largeN

A. Greco, R. Zeyher

Spin fluctuations enter the calculation of the superconducting transition temperature ${T}_{c}$ only in the next-to-leading order [i.e., in ${O(1/N}^{2})]$ of the $1/N$ expansion of the $t\ensuremath{-}J$ model. We have calculated these terms and show that they have only little influence on the value for ${T}_{c}$ obtained in the leading order $O(1/N)$ in the optimal and overdoped region, i.e., for dopings larger than the instability towards a flux phase. This result disagrees with recent spin-fluctuation mediated pairing theories. The discrepancies can be traced back to the fact that in our case the coupling between electrons and spins is determined by the $t\ensuremath{-}J$ model and not adjusted and that the spin susceptibility is rather broad and structureless and not strongly peaked at low energies as in spin-fluctuation models. Relating ${T}_{c}$ and transport we show that the effective interactions in the particle-particle and particle-hole channels are not simply related within the $1/N$ expansion by different Fermi surface averages of the same interaction as in the case of phonons or spin fluctuations. As a result, we find that large values for ${T}_{c}$ and rather small scattering rates in the normal state as found in the experiments can easily be reconciled with each other. We also show that correlation effects heavily suppress transport relaxation rates relative to quasiparticle relaxation rates in the case of phonons but not in the case of spin fluctuations.

arXiv:cond-mat/0011255•Physical review. B, Condensed matter•Jan 23, 2001•7 citations
The equation for the charge vertex \ensuremath{\gamma} of the t-J model is derived and solved in leading order of a 1/N expansion, working directly in terms of Hubbard operators. Various quantities which depend crucially on \ensuremath{\gamma} are then calculated, such as the lifetime and the transport lifetime of electrons due to a charge coupling to other degrees of freedom and the charge-charge correlation function. Our results show that the static screening of charges and the dynamics of charge fluctuations depend only weakly on J and are mainly determined by the constraint of having no double occupancies of sites. \textcopyright{} 1996 The American Physical Society.
Using the mapping of the single-occupation space of the t-J model onto the tensor-product space of local spin-1/2 and holon states, the Hubbard operators and their products corresponding to physical quantities are expressed in terms of local spin and holon operators. All relevant operator relations of the t-J model are reproduced by this representation and no projection procedure is needed to remove the redundant degrees of freedom originating from the spin and charge decoupling. It is shown that the time-reversal symmetry requirement makes the essential restriction on the choice of the fictitious spin state associated with the electron-vacancy state in the mapping. The results are critically compared with the treatment of this topic in the paper of Wang and Rice [Phys. Rev. B 49, 4360 (1994)]. \textcopyright{} 1996 The American Physical Society.
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a T2{\mathit{T}}^{2}T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.
We consider the dynamic charge susceptibility and the charge density waves in strongly-correlated electronic systems within the two-dimensional t-J-V model. Using the equation of motion method for the relaxation functions in terms of the Hubbard operators, we calculate the static susceptibility and the spectrum of charge fluctuations as functions of doped hole concentrations and temperature. Charge density waves emerge for a sufficiently strong intersite Coulomb interaction. Calculation of the dynamic charge susceptibility reveals a strong damping of charge density waves for a small hole doping and propagating high-energy charge excitations at large doping.
The dynamic charge susceptibility and the optical conductivity are calculated in the planar $t\ensuremath{-}J$ model within the memory function method, working directly in terms of Hubbard operators. The density fluctuation spectrum consists of a damped soundlike mode for small wave vectors and a broad high energy peak $(\ensuremath{\sim}t)$ for large momenta. The study of the optical conductivity shows that electron scattering from spin fluctuations leads to the Drude-frequency dependent relaxation rate which exhibits a crossover from ${\ensuremath{\omega}}^{3/2}$ behavior at low frequencies $(\ensuremath{\omega}<2|\ensuremath{\mu}|),$ to a linear $\ensuremath{\omega}$ dependence for frequencies larger than $2|\ensuremath{\mu}|.$ Due to the spin-polaron nature of charge carriers, extra absorptions arise starting at a frequency $\ensuremath{\omega}\ensuremath{\gtrsim}J.$ The obtained results are in a good agreement with exact diagonalization studies.
We show an exact representation of the t-J model by making use of a general Holstein-Primakoff transformation. The single occupancy constraint on the electrons is imposed strictly at every lattice site and the t-J Hamiltonian is transformed into an equivalent interacting boson and fermion system. The lowest-order approximation of a systematic perturbative expansion of the representation is shown to correspond to the mean-field theory of the Schwinger-boson approach. The second-order approximation gives the magnon-magnon, magnon-hole, and hole-hole interactions and the high-order antiferromagnetic spin polaron. In particular the second-order approximation takes further account of the renormalization of the magnon frequency and the antiferromagnetic spin polaron. The spectra of holes and magnons are calculated with the Green's function. The relevance of the obtained results to high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors is discussed. \textcopyright{} 1996 The American Physical Society.
Spin fluctuations enter the calculation of the superconducting transition temperature Tc{T}_{c}Tc​ only in the next-to-leading order [i.e., in O(1/N2)]{O(1/N}^{2})]O(1/N2)] of the 1/N1/N1/N expansion of the $t\ensuremath{-}J$ model. We have calculated these terms and show that they have only little influence on the value for Tc{T}_{c}Tc​ obtained in the leading order O(1/N)O(1/N)O(1/N) in the optimal and overdoped region, i.e., for dopings larger than the instability towards a flux phase. This result disagrees with recent spin-fluctuation mediated pairing theories. The discrepancies can be traced back to the fact that in our case the coupling between electrons and spins is determined by the $t\ensuremath{-}J$ model and not adjusted and that the spin susceptibility is rather broad and structureless and not strongly peaked at low energies as in spin-fluctuation models. Relating Tc{T}_{c}Tc​ and transport we show that the effective interactions in the particle-particle and particle-hole channels are not simply related within the 1/N1/N1/N expansion by different Fermi surface averages of the same interaction as in the case of phonons or spin fluctuations. As a result, we find that large values for Tc{T}_{c}Tc​ and rather small scattering rates in the normal state as found in the experiments can easily be reconciled with each other. We also show that correlation effects heavily suppress transport relaxation rates relative to quasiparticle relaxation rates in the case of phonons but not in the case of spin fluctuations.