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

Physical review. B, Condensed matter

Cluster study of thet-Jmodel: Chiral fluctuations

Didier Poilblanc, Elbio R. Dagotto, José A. Riera

Published Apr 1, 1991• 21 citations
Publisher

Abstract

Uniform and staggered chiral order are investigated in the two-dimensional t-J model at arbitrary doping fractions. Equal-time and dynamical correlations are calculated on a 4\ifmmode\times\else\texttimes\fi{}4 cluster by using a Lanczos algorithm. We found that static uniform correlations are suppressed with increasing doping and t/J while static staggered correlations seem enhanced, in agreement with previous mean-field studies. The plaquette-plaquette correlation function falls off rapidly with distance, and, thus, we obtain an upper bound on the plaquette order parameter, which is very small. However, our numerical results show that doping for t/J\ensuremath{\ge}1 induces large chiral fluctuations at low energy, which may become important even in the absence of long-range order. The staggered order parameter exhibits low-energy fluctuations of energy \ensuremath{\sim}2J, while for the uniform case fluctuations also occur at a higher energy \ensuremath{\sim}2t.

DOI
10.1103/physrevb.43.7899

Related papers

Static and dynamical properties of doped Hubbard clusters

Elbio R. Dagotto, Adriana Moreo, F. Ortolani +2 more

We study the t-J and the Hubbard models at zero temperature using exact-diagonalization techniques on \ensuremath{\surd}10 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}10 and 4\ifmmode\times\else\texttimes\fi{}4 sites clusters. Quantum Monte Carlo simulation results on larger lattices are also presented. All electronic fillings have been analyzed for the three models. We have measured equal-time correlation functions corresponding to various types of order (ranging from ``standard'' staggered spin order to more ``exotic'' possibilities like chiral order), as well as various dynamical properties of these models. Upper bounds for the critical hole doping (${\mathit{x}}_{\mathit{c}}$), where long-range antiferromagnetic order disappears, are presented. It was found that ${\mathit{x}}_{\mathit{c}}$ is very small in agreement with experiments for the high-${\mathit{T}}_{\mathit{c}}$ superconductors. For example, in the t-J model, ${\mathit{x}}_{\mathit{c}}$0.08 at J/t=0.4. However, short-distance spin correlations are important up to much higher dopings producing a sharp well-defined spin-wave-like peak in S(q=(\ensuremath{\pi},\ensuremath{\pi}),\ensuremath{\omega}). Regarding the possibility of phase separation in the Hubbard model, we have studied the behavior of the density of particles, 〈n〉, as a function of the chemical potential, using the Lanczos method on a 4\ifmmode\times\else\texttimes\fi{}4 Hubbard cluster, finding no indications of phase separation for any value of U/t. Then, we conclude that the t-J model at small J/t should not phase separate.In order to compare theoretical predictions with photoemission experiments, we evaluated the electronic density of states N(\ensuremath{\omega}), of the Hubbard and t-J models at several doping fractions. We found that upon doping the antiferromagnetic gap is filled for U\ensuremath{\sim}8t or smaller. The chemical potential moves across the insulating gap as one goes from electron to hole doping of the half-filled cluster, in agreement with x-ray absorption experiments but at variance with photoemission experiments. We have also calculated the optical conductivity, ${\mathrm{\ensuremath{\sigma}}}_{1}$(\ensuremath{\omega}), of the Hubbard and t-J models at all dopings on 4\ifmmode\times\else\texttimes\fi{}4 clusters. Results are compared with experiments and the weight of the Drude peak is presented as a function of couplings and dopings. Spectral weight found at small frequencies is associated with the mid-infrared band observed experimentally in ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$, and with the states filling the insulating gap in photoemission experiments. An overall good agreement with experiments in the normal state was found. Regarding the possibility of superconductivity n these models, we have studied s-, d-, and p-wave pairing correlations. Naively, the d-wave channel seems enhanced near half filling while the extended s-wave channel seems enhanced from half filling up to 40% doping.However, we found that the enhancement comes from short-distance effects and, thus, no numerical indications of superconductivity were found in these models. We emphasize the importance of analyzing the pairing correlations as a function of distance to distinguish between short- and long-distance effects in the susceptibilities. We also observed that spiral order is enhanced at small J/t and low doping. Uniform chiral rder is suppressed by dynamical holes while staggered chiral order may be enhanced, although with a small plaquette order parameter. We conclude with the observation that the simple one-band Hubbard model with intermediate values of U\ensuremath{\sim}8t may account for many of the ``anomalous'' properties of the normal state of the high-${\mathit{T}}_{\mathit{c}}$ superconductors.

Physical review. B, Condensed matter•May 1, 1992•201 citations

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.

Physical review. B, Condensed matter•Jan 15, 1995•1 citation

Magnetic fluctuations in the canted antiferromagnetic phase of at-Jmodel

G. C. Psaltakis, N. Papanicolaou

The dynamics of magnetic fluctuations in the canted antiferromagnetic phase of a t-J model is studied within a suitable 1/N expansion. We calculate the dynamical structure factor and assess the effect of hole doping on the excitation spectrum, the staggered antiferromagnetic moment, and the perpendicular uniform ferromagnetic moment. The average long-wavelength excitation energies in the transverse direction are shown to soften with increasing hole concentration, in qualitative agreement with recent neutron-scattering experiments in doped antiferromagnets.

Physical review. B, Condensed matter•Dec 1, 1990•3 citations

Spin diffusion of thet-Jmodel

J. Bonča, Janez Jaklič

The spin-diffusion constant of the two-dimensional t-J model is calculated using an analytical approach at high temperatures and a recently developed numerical method based on the Lanczos technique combined with random sampling in the intermediate temperature regime. A simple relation, \ensuremath{\sigma}=${\mathit{D}}_{\mathit{s}}$\ensuremath{\chi}, between spin conductivity and spin diffusion is established and used to calculate the latter. In the high-temperature and low-doping limit, the calculated diffusion constant agrees with known results for the Heisenberg model. At small hole doping, ${\mathit{D}}_{\mathit{s}}$ increases approximately linearly with doping, which leads us to an important conclusion that hopping processes enhance spin diffusion at high temperatures. At modest hole doping, \ensuremath{\delta}\ensuremath{\sim}0.25, diffusion exhibits a nonmonotonic temperature dependence, which indicates anomalous spin dynamics at small frequencies.

arXiv:cond-mat/9412055•Physical review. B, Condensed matter•Jun 1, 1995•16 citations

Static and dynamical correlations in a spin-1/2 frustrated antiferromagnet

Didier Poilblanc, Eduardo R. Gagliano, Silvia Bacci +1 more

We study the frustrated spin-1/2 antiferromagnetic Heisenberg model on a square lattice of 16 sites, using a Lanczos algorithm and group-theoretical techniques. We investigate the competition between collinear, dimer, chiral, and spiral orders by calculating the dynamical and spatial correlation functions. Our numerical results strongly suggest the presence of long-range collinear order in the interval 0.55\ensuremath{\le}${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\le}0.9 (we cannot show numerically that this order exists for larger values of ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$). Dimer- and chiral-order parameters both show increasing low-energy fluctuations and a longer range of the correlations in space around ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\sim}0.55. We propose an order parameter for chiral order exhibiting the full symmetry of the cluster and hence being less sensitive to finite-size effects. The mean value of the square of this plaquette chiral-order parameter is enhanced for ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\sim}0.55, where the characteristic chiral spin-fluctuation frequency is reduced, but no indications of long-range chiral order were found. Although the correlation function of the twist-order parameter is not a simple monotonically decreasing function of distance, little change is induced by frustration, suggesting that spiral order is not strongly favored. The energy gap corresponding to dimer order is smaller than those of spin waves, spiral order, and chiral order; thus, this state is the best candidate for an intermediate-(${\mathit{J}}_{2}$/${\mathit{J}}_{1}$) phase in the ${\mathit{J}}_{1}$-${\mathit{J}}_{2}$ model.

Physical review. B, Condensed matter•May 1, 1991•43 citations

Doping dependence of the Fermi surface in thet-Jmodel

Stephan Haas

The evolution of the Fermi surface upon hole doping is studied in the t-J model of correlated electrons by exact diagonalization of chains and planes. In one dimension at low hole doping, the momentum distribution function n(k) indicates the presence of pocketlike features at the (noninteracting) Fermi momentum, while increasing the density of holes a large Fermi surface is observed. Although the results in two dimensions are consistent with this picture, conclusive evidence for the existence of hole pockets (at intermediate doping levels) cannot be provided in the present study of 4\ifmmode\times\else\texttimes\fi{}4 and \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 square lattices. In order to improve the resolution in momentum space, twisted boundary conditions are used for the two-dimensional clusters.

Physical review. B, Condensed matter•May 1, 1995•6 citations
Uniform and staggered chiral order are investigated in the two-dimensional t-J model at arbitrary doping fractions. Equal-time and dynamical correlations are calculated on a 4\ifmmode\times\else\texttimes\fi{}4 cluster by using a Lanczos algorithm. We found that static uniform correlations are suppressed with increasing doping and t/J while static staggered correlations seem enhanced, in agreement with previous mean-field studies. The plaquette-plaquette correlation function falls off rapidly with distance, and, thus, we obtain an upper bound on the plaquette order parameter, which is very small. However, our numerical results show that doping for t/J\ensuremath{\ge}1 induces large chiral fluctuations at low energy, which may become important even in the absence of long-range order. The staggered order parameter exhibits low-energy fluctuations of energy \ensuremath{\sim}2J, while for the uniform case fluctuations also occur at a higher energy \ensuremath{\sim}2t.
We study the t-J and the Hubbard models at zero temperature using exact-diagonalization techniques on \ensuremath{\surd}10 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}10 and 4\ifmmode\times\else\texttimes\fi{}4 sites clusters. Quantum Monte Carlo simulation results on larger lattices are also presented. All electronic fillings have been analyzed for the three models. We have measured equal-time correlation functions corresponding to various types of order (ranging from ``standard'' staggered spin order to more ``exotic'' possibilities like chiral order), as well as various dynamical properties of these models. Upper bounds for the critical hole doping (xc{\mathit{x}}_{\mathit{c}}xc​), where long-range antiferromagnetic order disappears, are presented. It was found that xc{\mathit{x}}_{\mathit{c}}xc​ is very small in agreement with experiments for the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors. For example, in the t-J model, ${\mathit{x}}_{\mathit{c}}$0.08 at J/t=0.4. However, short-distance spin correlations are important up to much higher dopings producing a sharp well-defined spin-wave-like peak in S(q=(\ensuremath{\pi},\ensuremath{\pi}),\ensuremath{\omega}). Regarding the possibility of phase separation in the Hubbard model, we have studied the behavior of the density of particles, 〈n〉, as a function of the chemical potential, using the Lanczos method on a 4\ifmmode\times\else\texttimes\fi{}4 Hubbard cluster, finding no indications of phase separation for any value of U/t. Then, we conclude that the t-J model at small J/t should not phase separate.In order to compare theoretical predictions with photoemission experiments, we evaluated the electronic density of states N(\ensuremath{\omega}), of the Hubbard and t-J models at several doping fractions. We found that upon doping the antiferromagnetic gap is filled for U\ensuremath{\sim}8t or smaller. The chemical potential moves across the insulating gap as one goes from electron to hole doping of the half-filled cluster, in agreement with x-ray absorption experiments but at variance with photoemission experiments. We have also calculated the optical conductivity, ${\mathrm{\ensuremath{\sigma}}}_{1}$(\ensuremath{\omega}), of the Hubbard and t-J models at all dopings on 4\ifmmode\times\else\texttimes\fi{}4 clusters. Results are compared with experiments and the weight of the Drude peak is presented as a function of couplings and dopings. Spectral weight found at small frequencies is associated with the mid-infrared band observed experimentally in ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4{\mathrm{CuO}}_{4}CuO4​, and with the states filling the insulating gap in photoemission experiments. An overall good agreement with experiments in the normal state was found. Regarding the possibility of superconductivity n these models, we have studied s-, d-, and p-wave pairing correlations. Naively, the d-wave channel seems enhanced near half filling while the extended s-wave channel seems enhanced from half filling up to 40% doping.However, we found that the enhancement comes from short-distance effects and, thus, no numerical indications of superconductivity were found in these models. We emphasize the importance of analyzing the pairing correlations as a function of distance to distinguish between short- and long-distance effects in the susceptibilities. We also observed that spiral order is enhanced at small J/t and low doping. Uniform chiral rder is suppressed by dynamical holes while staggered chiral order may be enhanced, although with a small plaquette order parameter. We conclude with the observation that the simple one-band Hubbard model with intermediate values of U\ensuremath{\sim}8t may account for many of the ``anomalous'' properties of the normal state of the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors.
We study contributions to the spin-exchange scattering amplitude at two-loop (1/N2{\mathit{N}}^{2}N2) 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.
The dynamics of magnetic fluctuations in the canted antiferromagnetic phase of a t-J model is studied within a suitable 1/N expansion. We calculate the dynamical structure factor and assess the effect of hole doping on the excitation spectrum, the staggered antiferromagnetic moment, and the perpendicular uniform ferromagnetic moment. The average long-wavelength excitation energies in the transverse direction are shown to soften with increasing hole concentration, in qualitative agreement with recent neutron-scattering experiments in doped antiferromagnets.
The spin-diffusion constant of the two-dimensional t-J model is calculated using an analytical approach at high temperatures and a recently developed numerical method based on the Lanczos technique combined with random sampling in the intermediate temperature regime. A simple relation, \ensuremath{\sigma}=Ds{\mathit{D}}_{\mathit{s}}Ds​\ensuremath{\chi}, between spin conductivity and spin diffusion is established and used to calculate the latter. In the high-temperature and low-doping limit, the calculated diffusion constant agrees with known results for the Heisenberg model. At small hole doping, Ds{\mathit{D}}_{\mathit{s}}Ds​ increases approximately linearly with doping, which leads us to an important conclusion that hopping processes enhance spin diffusion at high temperatures. At modest hole doping, \ensuremath{\delta}\ensuremath{\sim}0.25, diffusion exhibits a nonmonotonic temperature dependence, which indicates anomalous spin dynamics at small frequencies.
We study the frustrated spin-1/2 antiferromagnetic Heisenberg model on a square lattice of 16 sites, using a Lanczos algorithm and group-theoretical techniques. We investigate the competition between collinear, dimer, chiral, and spiral orders by calculating the dynamical and spatial correlation functions. Our numerical results strongly suggest the presence of long-range collinear order in the interval 0.55\ensuremath{\le}J2{\mathit{J}}_{2}J2​/J1{\mathit{J}}_{1}J1​\ensuremath{\le}0.9 (we cannot show numerically that this order exists for larger values of J2{\mathit{J}}_{2}J2​/J1{\mathit{J}}_{1}J1​). Dimer- and chiral-order parameters both show increasing low-energy fluctuations and a longer range of the correlations in space around J2{\mathit{J}}_{2}J2​/J1{\mathit{J}}_{1}J1​\ensuremath{\sim}0.55. We propose an order parameter for chiral order exhibiting the full symmetry of the cluster and hence being less sensitive to finite-size effects. The mean value of the square of this plaquette chiral-order parameter is enhanced for J2{\mathit{J}}_{2}J2​/J1{\mathit{J}}_{1}J1​\ensuremath{\sim}0.55, where the characteristic chiral spin-fluctuation frequency is reduced, but no indications of long-range chiral order were found. Although the correlation function of the twist-order parameter is not a simple monotonically decreasing function of distance, little change is induced by frustration, suggesting that spiral order is not strongly favored. The energy gap corresponding to dimer order is smaller than those of spin waves, spiral order, and chiral order; thus, this state is the best candidate for an intermediate-(J2{\mathit{J}}_{2}J2​/J1{\mathit{J}}_{1}J1​) phase in the J1{\mathit{J}}_{1}J1​-J2{\mathit{J}}_{2}J2​ model.
The evolution of the Fermi surface upon hole doping is studied in the t-J model of correlated electrons by exact diagonalization of chains and planes. In one dimension at low hole doping, the momentum distribution function n(k) indicates the presence of pocketlike features at the (noninteracting) Fermi momentum, while increasing the density of holes a large Fermi surface is observed. Although the results in two dimensions are consistent with this picture, conclusive evidence for the existence of hole pockets (at intermediate doping levels) cannot be provided in the present study of 4\ifmmode\times\else\texttimes\fi{}4 and \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 square lattices. In order to improve the resolution in momentum space, twisted boundary conditions are used for the two-dimensional clusters.