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

Ferromagnetism in the two-dimensionalt-Jmodel

Didier Poilblanc

Published May 1, 1992• 5 citations
Publisher

Abstract

The behavior of the Drude weight is studied in the small-J/t regime of the t-J model by Lanczos diagonalizations of small clusters with arbitrary boundary conditions and a small number of holes. Although the total spin of the ground state in the J/t\ensuremath{\rightarrow}0 limit depends strongly on the boundary conditions, the Drude weight exhibits a rather universal behavior and indicates a sharp transition around J/t\ensuremath{\sim}0.1 for a hole concentration of \ensuremath{\sim}10%. This crossover is interpreted as a paramagnetic-ferromagnetic transition. For J/t larger than the crossover value, the Drude weight is somehow constant (and reduced by a factor \ensuremath{\sim}3 compared to the case of free holes), suggesting that coherent transport is almost insensitive to the variation of the antiferromagnetic correlation length. At small J/t (and finite doping), the exact nature of the ferromagnetic phase is still uncertain, since both fully polarized state or spin-polaron gas are found in small clusters depending on the boundaries.

DOI
10.1103/physrevb.45.10775

Related papers

Phase diagram of the two-dimensionalt-Jmodel at low doping

Didier Poilblanc

The phase diagram of the planar t-J model at small hole doping is investigated by finite-size scaling of exact diagonalization data of \ensuremath{\surd}N \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}N clusters (N\ensuremath{\le}26). Hole-droplet binding energies, compressibility, and static spin and charge correlations are calculated. Short-range antiferromagnetic correlations can produce attractive forces between holes leading to a very rich phase diagram including a liquid of d-wave hole pairs (for J/t\ensuremath{\gtrsim}0.2), a liquid of hole droplets (quartets) for larger J/t ratios (J/t\ensuremath{\gtrsim}0.5), and, at even larger coupling J/t, an instability towards phase separation.

arXiv:cond-mat/9505004•Physical review. B, Condensed matter•Oct 1, 1995•42 citations

Ground-state properties and dynamics of the bilayert-Jmodel

R. Eder, Yutaka Ohta, Sadamichi Maekawa

We present an exact diagonalization study of bilayer clusters of the t-J model. Our results indicate a crossover between two markedly different regimes which occurs when the ratio ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J between interlayer and intralayer exchange constants increases: for small ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J the data suggest the development of three-dimensional antiferromagnetic correlations without appreciable degradation of the intralayer spin order and the ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ hole pairs within the planes persist. For larger values of ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J local singlets along the interlayer bonds dominate, leading to an almost complete suppression of the intralayer spin correlation and the breaking of the intralayer hole pairs. The ground state with two holes in this regime has s-like symmetry. We present data for static spin correlation function, magnetic structure factor, and spin gap. We calculate the momentum distribution and electronic spectral function of the ``local singlet state'' realized for large ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J, and show that it deviates markedly from that of a single layer, making it an implausible candidate for modeling high-temperature superconductors.

arXiv:cond-mat/9504013•Physical review. B, Condensed matter•Sep 1, 1995•15 citations

Precursory Metal-Insulator transition in a small cluster of the `t-J' model: Exact analytic results

Rogério de Sousa, G. G. Cabrera

We study the effect of hole hopping in a doped antiferromagnet described by the `t-J' model, using exact analytic solutions for small clusters. In spite of the small size, they reveal interesting details about the magnetic order, which are not apparent in Mean Field treatments or in numerical calculations. The 4-site cluster with one hole yields the most interesting physics, displaying different behaviors for the ground state: i) an antiferromagnetic phase for t<>J, we obtain strong ferromagnetic correlations (maximum spin) and no density waves, with quantum fluctuations precluding the saturation of the magnetic moment. This behavior shows traces of a metal-insulator transition as the hole kinetic energy competes with the antiferromagnetic interactions.

arXiv:cond-mat/0008373•Aug 24, 2000•0 citations

Ferromagnetic polarons in a one-dimensionalt-Jmodel with next-nearest-neighbor hopping

P. Prelovek, A. Ramak, Igor Sega

In a t-J model on a chain, an additional next-nearest-neighbor hopping term destroys the complete spin-charge separation at J/t\ensuremath{\ll}1 and induces the formation of stable spin-polarized S>0 states. The properties of a single ferromagnetic polaron are investigated by the exact diagonalization of small systems and by the approximative treatment of an effective model, describing a spinless fermion coupled to the spin background. Both methods give consistent results on the critical ${\mathit{J}}_{\mathit{c}}$ for the polaron formation on the increase of the spin S and the polaron size with decreasing J. A very large enhancement of the polaron mass with increasing S is observed. Systems with a finite concentration of holes are also studied within the same framework. Analytical considerations indicate on the bound many-hole states and consequently on phase-separated regions in the phase diagram.

Physical review. B, Condensed matter•Dec 1, 1991•5 citations

Twisted boundary conditions in cluster calculations of the optical conductivity in two-dimensional lattice models

Didier Poilblanc

We investigate the extended t-J model (which may include a small next-nearest-neighbor antiferromagnetic coupling or a small hole-hole nearest-neighbor repulsion) by exact-diagonalization techniques. The calculation is done for one and two holes on a 4\ifmmode\times\else\texttimes\fi{}4 torus with arbitrary twisted boundary conditions. The role of the boundary conditions on the ground-state energy, the band width, the charge stiffness, and the optical conductivity is extensively studied. In the two-dimensional space of the twist angles (to be viewed as fluxes through the holes of the torus) the ground-state energy surface exhibits multiple level crossings and may present, locally, a negative curvature (or stiffness) characteristic of a paramagnetic behavior. For two holes and sufficiently large J/t (J/t>0.7) the minima of the energy surface in the parameter space of the fluxes are separated by half a flux quantum. The optical conductivity is calculated by averaging over the boundary conditions in order to minimize finite-size effects and to converge more rapidly toward the thermodynamic limit. We find three different contributions to the optical conductivity; (i) a Drude peak at \ensuremath{\omega}=0, (ii) a broad absorption band in the range J2t, and (iii) a tail extending to larger frequencies (2t7t) associated to the diffusive character of the hole states at these energies.Typically, at low doping density (6%) for a wide range of J/t, and at intermediate doping (12%) for small J/t, these three components account for roughly 30%, 50%, and 20% of the total spectral weight, respectively. At small ratio J/t, both Drude weight and finite-frequency absorption scale almost proportionally with the doping density. However, with increasing J/t, the effective hole-hole attraction (for 12% doping) leads to a transfer of weight from finite frequency to zero frequency. In contrast to the quasiparticle mass, in the J/t\ensuremath{\rightarrow}0 limit, the optical mass defined through the weight of the Drude \ensuremath{\delta}-function peak does not increase like \ensuremath{\sim}t/J but, rather, approaches a limit around \ensuremath{\sim}5. We discuss our results in connection with the optical experiments in the high-${\mathit{T}}_{\mathit{c}}$ cuprates and suggest that the observed mid-infrared band is due to the strong coupling between the mobile holes and the spin excitations of the Mott insulator, as expected from a description in terms of the t-J Hamiltonian.

Physical review. B, Condensed matter•Nov 1, 1991•137 citations

Binding of holes and the pair spectral function in thet-Jmodel

Didier Poilblanc

Clusters of the two-dimensional t-J model with two holes and up to 26 sites are diagonalized using a Lanczos algorithm. The behavior of the binding energy with system size suggests the existence of a finite critical value of J above which binding occurs in the bulk. Only the d-wave pair-field operator acting on the Heisenberg ground state has a finite overlap with the two-hole ground state for all the clusters considered. The related spectral function associated with the propagation of a d-wave (singlet) pair of holes in the antiferromagnetic background is calculated. The quasiparticle peak at the bottom of the spectrum as well as some structure appearing above the peak survive with increasing cluster size. Although no simple scaling law was found for the quasiparticle weight the data strongly suggest that this weight is finite in the bulk limit and is roughly proportional to the antiferromagnetic coupling J (for J1).

arXiv:cond-mat/9303029•Physical review. B, Condensed matter•Aug 1, 1993•49 citations
The behavior of the Drude weight is studied in the small-J/t regime of the t-J model by Lanczos diagonalizations of small clusters with arbitrary boundary conditions and a small number of holes. Although the total spin of the ground state in the J/t\ensuremath{\rightarrow}0 limit depends strongly on the boundary conditions, the Drude weight exhibits a rather universal behavior and indicates a sharp transition around J/t\ensuremath{\sim}0.1 for a hole concentration of \ensuremath{\sim}10%. This crossover is interpreted as a paramagnetic-ferromagnetic transition. For J/t larger than the crossover value, the Drude weight is somehow constant (and reduced by a factor \ensuremath{\sim}3 compared to the case of free holes), suggesting that coherent transport is almost insensitive to the variation of the antiferromagnetic correlation length. At small J/t (and finite doping), the exact nature of the ferromagnetic phase is still uncertain, since both fully polarized state or spin-polaron gas are found in small clusters depending on the boundaries.
The phase diagram of the planar t-J model at small hole doping is investigated by finite-size scaling of exact diagonalization data of \ensuremath{\surd}N \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}N clusters (N\ensuremath{\le}26). Hole-droplet binding energies, compressibility, and static spin and charge correlations are calculated. Short-range antiferromagnetic correlations can produce attractive forces between holes leading to a very rich phase diagram including a liquid of d-wave hole pairs (for J/t\ensuremath{\gtrsim}0.2), a liquid of hole droplets (quartets) for larger J/t ratios (J/t\ensuremath{\gtrsim}0.5), and, at even larger coupling J/t, an instability towards phase separation.
We present an exact diagonalization study of bilayer clusters of the t-J model. Our results indicate a crossover between two markedly different regimes which occurs when the ratio ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J between interlayer and intralayer exchange constants increases: for small ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J the data suggest the development of three-dimensional antiferromagnetic correlations without appreciable degradation of the intralayer spin order and the dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2 hole pairs within the planes persist. For larger values of ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J local singlets along the interlayer bonds dominate, leading to an almost complete suppression of the intralayer spin correlation and the breaking of the intralayer hole pairs. The ground state with two holes in this regime has s-like symmetry. We present data for static spin correlation function, magnetic structure factor, and spin gap. We calculate the momentum distribution and electronic spectral function of the ``local singlet state'' realized for large ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J, and show that it deviates markedly from that of a single layer, making it an implausible candidate for modeling high-temperature superconductors.
We study the effect of hole hopping in a doped antiferromagnet described by the `t-J' model, using exact analytic solutions for small clusters. In spite of the small size, they reveal interesting details about the magnetic order, which are not apparent in Mean Field treatments or in numerical calculations. The 4-site cluster with one hole yields the most interesting physics, displaying different behaviors for the ground state: i) an antiferromagnetic phase for t<>J, we obtain strong ferromagnetic correlations (maximum spin) and no density waves, with quantum fluctuations precluding the saturation of the magnetic moment. This behavior shows traces of a metal-insulator transition as the hole kinetic energy competes with the antiferromagnetic interactions.
In a t-J model on a chain, an additional next-nearest-neighbor hopping term destroys the complete spin-charge separation at J/t\ensuremath{\ll}1 and induces the formation of stable spin-polarized S>0 states. The properties of a single ferromagnetic polaron are investigated by the exact diagonalization of small systems and by the approximative treatment of an effective model, describing a spinless fermion coupled to the spin background. Both methods give consistent results on the critical Jc{\mathit{J}}_{\mathit{c}}Jc​ for the polaron formation on the increase of the spin S and the polaron size with decreasing J. A very large enhancement of the polaron mass with increasing S is observed. Systems with a finite concentration of holes are also studied within the same framework. Analytical considerations indicate on the bound many-hole states and consequently on phase-separated regions in the phase diagram.
We investigate the extended t-J model (which may include a small next-nearest-neighbor antiferromagnetic coupling or a small hole-hole nearest-neighbor repulsion) by exact-diagonalization techniques. The calculation is done for one and two holes on a 4\ifmmode\times\else\texttimes\fi{}4 torus with arbitrary twisted boundary conditions. The role of the boundary conditions on the ground-state energy, the band width, the charge stiffness, and the optical conductivity is extensively studied. In the two-dimensional space of the twist angles (to be viewed as fluxes through the holes of the torus) the ground-state energy surface exhibits multiple level crossings and may present, locally, a negative curvature (or stiffness) characteristic of a paramagnetic behavior. For two holes and sufficiently large J/t (J/t>0.7) the minima of the energy surface in the parameter space of the fluxes are separated by half a flux quantum. The optical conductivity is calculated by averaging over the boundary conditions in order to minimize finite-size effects and to converge more rapidly toward the thermodynamic limit. We find three different contributions to the optical conductivity; (i) a Drude peak at \ensuremath{\omega}=0, (ii) a broad absorption band in the range J2t, and (iii) a tail extending to larger frequencies (2t7t) associated to the diffusive character of the hole states at these energies.Typically, at low doping density (6%) for a wide range of J/t, and at intermediate doping (12%) for small J/t, these three components account for roughly 30%, 50%, and 20% of the total spectral weight, respectively. At small ratio J/t, both Drude weight and finite-frequency absorption scale almost proportionally with the doping density. However, with increasing J/t, the effective hole-hole attraction (for 12% doping) leads to a transfer of weight from finite frequency to zero frequency. In contrast to the quasiparticle mass, in the J/t\ensuremath{\rightarrow}0 limit, the optical mass defined through the weight of the Drude \ensuremath{\delta}-function peak does not increase like \ensuremath{\sim}t/J but, rather, approaches a limit around \ensuremath{\sim}5. We discuss our results in connection with the optical experiments in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates and suggest that the observed mid-infrared band is due to the strong coupling between the mobile holes and the spin excitations of the Mott insulator, as expected from a description in terms of the t-J Hamiltonian.
Clusters of the two-dimensional t-J model with two holes and up to 26 sites are diagonalized using a Lanczos algorithm. The behavior of the binding energy with system size suggests the existence of a finite critical value of J above which binding occurs in the bulk. Only the d-wave pair-field operator acting on the Heisenberg ground state has a finite overlap with the two-hole ground state for all the clusters considered. The related spectral function associated with the propagation of a d-wave (singlet) pair of holes in the antiferromagnetic background is calculated. The quasiparticle peak at the bottom of the spectrum as well as some structure appearing above the peak survive with increasing cluster size. Although no simple scaling law was found for the quasiparticle weight the data strongly suggest that this weight is finite in the bulk limit and is roughly proportional to the antiferromagnetic coupling J (for J1).