© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Physical review. B, Condensed matter

Charge and spin structures in the one-dimensionalt-Jmodel

Fakher F. Assaad, Diethelm Würtz

Published Aug 1, 1991• 57 citations

Abstract

The physics of the one-dimensional t-J model may be determined at J/t\ensuremath{\rightarrow}0 (i.e., the U/t\ensuremath{\rightarrow}\ensuremath{\infty} limit of the repulsive Hubbard model) and at J/t=2 with the use of the Bethe ansatz. To get a full understanding of the charge and spin correlation functions for all values of J/t, one has to resort to numerical methods. We have used two numerical methods (the world-line quantum Monte Carlo algorithm and the quantum transfer-matrix algorithm) to get information on charge and spin static structure factors, pairing correlations, and critical exponents. The (1+1)-dimensional classical system corresponding to the one-dimensional t-J model, on which the Monte Carlo technique is used, is identified to a fifteen-vertex model. We show that the t-J model undergoes phase separation at large values of J/t. Before phase separation, both critical exponents and pairing correlations in the extended s-wave channel favor the onset of superconductivity. For low values of J/t, the model shows a U/t\ensuremath{\rightarrow}\ensuremath{\infty} Hubbard-like character.

DOI: 10.1103/physrevb.44.2681

Related papers

Spin and charge dynamics for the one-dimensionalt-Jmodel

J. J. Deisz, K.-H. Luk, Mark Jarrell +1 more

The dynamic spin and charge correlation functions are computed for the one-dimensional t-J model with use of world-line quantum Monte Carlo and the maximum-entropy method. By comparing our results with exactly known limits, we are able to discern the power and limitations of this method. The spin excitation spectrum shows gapless spin excitations for q=2${\mathit{k}}_{\mathit{F}}$ when J\ensuremath{\le}2t and for q=\ensuremath{\pi} when J>3.25t where phase separation occurs. Also, intermediate values of J/t show no spin gap for the large electron filling (${\mathrm{\ensuremath{\rho}}}_{0}$=0.75) considered here. For J\ensuremath{\le}2t, the charge correlations are dominated at high frequencies by excitations which are related to the particle-hole excitations found for J=0, but a low-frequency mode appears at finite values of J, which is likely related to the binding of electron pairs.

Physical review. B, Condensed matter•Aug 1, 1992•9 citations

Correlation functions in the one-dimensionalt-Jmodel

Norio Kawakami, Sung-Kil Yang

The critical exponents for the charge, spin, electron, and superconducting correlation functions of the one-dimensional t-J model at t=J are obtained for arbitrary band filling. Our method is based on the Bethe-ansatz solution and the finite-size scaling analysis in conformal field theory. The long-distance behavior of the model belongs to the same universality class as the repulsive Hubbard model. Near half-filling the exponents take the values expected in the strong-correlation limit of the Hubbard model. In the low-density limit the exponents are those of the noninteracting system.

Physical Review Letters•Oct 29, 1990•169 citations

Numerical Studies on the Hubbard Model and thet-JModel in One- and Two-Dimensions

Masatoshi Imada, Yasuhiro Hatsugai

Numerical results obtained from Monte Carlo simulation in the ground state and at finite temperatures as well as the exact diagonalization and the transfer matrix method are reported. Efficiency of the Monte Carlo method in the ground state is examined. Spin, charge and superconducting correlations are investigated for the Hubbard and the t - J model in one and two dimensions. The momentum distribution in the one-dimensional Hubbard model shows fermi-liquid-like behavior at least in two orders of magnitude smaller energy scale than the band width. The short-range incommensurate spin correlation is observed and analyzed in the doped Hubbard and the t - J model both in one and two dimensions. In the ground state, the superconducting correlation shows the absence of system size dependence in two dimensions at the filling smaller than 0.8 and in one dimension at any filling. The binding energy of two fermions and the spin and charge distortion around an itinerant fermion are also discussed in the t - J and the coupled spin-fermion model.

Journal of the Physical Society of Japan•Oct 15, 1989•227 citations

Variational study of the spin-gap phase of the one-dimensionalt-Jmodel

Y. C. Chen, T. K. Lee

We propose a correlated spin-singlet-pair wave function to describe the spin-gap phase of the one-dimensional t-J model at low density and large J/t. In addition to having singlet pairs, this wave function has a Jastrow factor with a variational parameter \ensuremath{\nu}. Several correlation functions are calculated by using the variational Monte Carlo method. The result shows the expected long-range behavior of the Luther-Emery phase with the Luttinger exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ related to \ensuremath{\nu}, ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$=1/2\ensuremath{\nu}. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9604191•Physical review. B, Condensed matter•Oct 1, 1996•9 citations

Spin-charge separation in the two-dimensional Hubbard andt-Jmodels at low electronic density

Y.-C. Chen, Adriana Moreo, F. Ortolani +2 more

The spin- and density-correlation functions of the two-dimensional Hubbard model at low electronic density 〈n〉 are calculated in the ground state by using the power method, and at finite temperatures by using the quantum Monte Carlo technique. Both approaches produce similar results, which are in close agreement with numerical and high-temperature-expansion results for the two-dimensional t-J model. Using perturbative approximations, we show that the examination of the density-correlation function alone is not enough to support recent claims in the literature that suggested spin and charge separation in the low electronic density regime of the t-J model.

arXiv:cond-mat/9403037•Physical review. B, Condensed matter•Jul 1, 1994•42 citations

Spin gap and superconductivity in the one-dimensionalt-Jmodel with Coulomb repulsion

Matthias Troyer, Hirokazu Tsunetsugu, Thomas Maurice Rice +2 more

The one-dimensional t-J model with density-density repulsive interactions is investigated with the use of exact-diagonalization and quantum Monte Carlo methods. A short-range repulsion pushes phase separation to larger values of J/t, and leads to a widened precursor region in which a spin gap and strengthened superconducting correlations appear. The correlation exponent is calculated. On the contrary, a long-range repulsion of form 1/r suppresses superconductivity in the precursor region.

arXiv:cond-mat/9212031•Physical review. B, Condensed matter•Aug 1, 1993•32 citations

The physics of the one-dimensional t-J model may be determined at J/t\ensuremath{\rightarrow}0 (i.e., the U/t\ensuremath{\rightarrow}\ensuremath{\infty} limit of the repulsive Hubbard model) and at J/t=2 with the use of the Bethe ansatz. To get a full understanding of the charge and spin correlation functions for all values of J/t, one has to resort to numerical methods. We have used two numerical methods (the world-line quantum Monte Carlo algorithm and the quantum transfer-matrix algorithm) to get information on charge and spin static structure factors, pairing correlations, and critical exponents. The (1+1)-dimensional classical system corresponding to the one-dimensional t-J model, on which the Monte Carlo technique is used, is identified to a fifteen-vertex model. We show that the t-J model undergoes phase separation at large values of J/t. Before phase separation, both critical exponents and pairing correlations in the extended s-wave channel favor the onset of superconductivity. For low values of J/t, the model shows a U/t\ensuremath{\rightarrow}\ensuremath{\infty} Hubbard-like character.

The dynamic spin and charge correlation functions are computed for the one-dimensional t-J model with use of world-line quantum Monte Carlo and the maximum-entropy method. By comparing our results with exactly known limits, we are able to discern the power and limitations of this method. The spin excitation spectrum shows gapless spin excitations for q=2

{\mathit{k}}_{\mathit{F}}

when J\ensuremath{\le}2t and for q=\ensuremath{\pi} when J>3.25t where phase separation occurs. Also, intermediate values of J/t show no spin gap for the large electron filling (${\mathrm{\ensuremath{\rho}}}_{0}$=0.75) considered here. For J\ensuremath{\le}2t, the charge correlations are dominated at high frequencies by excitations which are related to the particle-hole excitations found for J=0, but a low-frequency mode appears at finite values of J, which is likely related to the binding of electron pairs.

The critical exponents for the charge, spin, electron, and superconducting correlation functions of the one-dimensional t-J model at t=J are obtained for arbitrary band filling. Our method is based on the Bethe-ansatz solution and the finite-size scaling analysis in conformal field theory. The long-distance behavior of the model belongs to the same universality class as the repulsive Hubbard model. Near half-filling the exponents take the values expected in the strong-correlation limit of the Hubbard model. In the low-density limit the exponents are those of the noninteracting system.

Numerical results obtained from Monte Carlo simulation in the ground state and at finite temperatures as well as the exact diagonalization and the transfer matrix method are reported. Efficiency of the Monte Carlo method in the ground state is examined. Spin, charge and superconducting correlations are investigated for the Hubbard and the t - J model in one and two dimensions. The momentum distribution in the one-dimensional Hubbard model shows fermi-liquid-like behavior at least in two orders of magnitude smaller energy scale than the band width. The short-range incommensurate spin correlation is observed and analyzed in the doped Hubbard and the t - J model both in one and two dimensions. In the ground state, the superconducting correlation shows the absence of system size dependence in two dimensions at the filling smaller than 0.8 and in one dimension at any filling. The binding energy of two fermions and the spin and charge distortion around an itinerant fermion are also discussed in the t - J and the coupled spin-fermion model.

We propose a correlated spin-singlet-pair wave function to describe the spin-gap phase of the one-dimensional t-J model at low density and large J/t. In addition to having singlet pairs, this wave function has a Jastrow factor with a variational parameter \ensuremath{\nu}. Several correlation functions are calculated by using the variational Monte Carlo method. The result shows the expected long-range behavior of the Luther-Emery phase with the Luttinger exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ related to \ensuremath{\nu}, ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$=1/2\ensuremath{\nu}. \textcopyright{} 1996 The American Physical Society.

The spin- and density-correlation functions of the two-dimensional Hubbard model at low electronic density 〈n〉 are calculated in the ground state by using the power method, and at finite temperatures by using the quantum Monte Carlo technique. Both approaches produce similar results, which are in close agreement with numerical and high-temperature-expansion results for the two-dimensional t-J model. Using perturbative approximations, we show that the examination of the density-correlation function alone is not enough to support recent claims in the literature that suggested spin and charge separation in the low electronic density regime of the t-J model.