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

One-dimensionalt-Jand Hubbard models in a staggered field

Peter Prelovšek, Igor Sega, J. Bonča, H. Q. Lin, David K Campbell

Published May 1, 1993• 4 citations
Publisher

Abstract

The influence of the staggered magnetic field h on properties of the one-dimensional t-J and Hubbard models with nearly half-filled bands are studied. Using the exact diagonalization method for small systems as well as analytical approaches possible in the anisotropic model and for h\ensuremath{\gg}t, we determine the phase diagram of the t-J-h model at low doping, which displays three different regimes: the phase with repelling holes for J${\mathit{J}}_{\mathit{c}}$, the phase with paired holes for ${\mathit{J}}_{\mathit{c}}$J${\mathit{J}}_{\mathit{s}}$, and the phase separation for J>${\mathit{J}}_{\mathit{s}}$. Employing for h\ensuremath{\ne}0 the analogy with the universal behavior of one-dimensional interacting fermions within the Luther-Emery regime, we calculate the charge exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$, which can be ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$>1 in the pairing regime, indicating dominant superconducting fluctuations. An analogous analysis, in particular the perturbation expansion in t/h, performed for the Hubbard t-U-h model shows a phase of stable hole pairs for U${\mathit{U}}_{\mathit{c}}$. Again ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ seems to approach a nonuniversal value at half-filling.

DOI
10.1103/physrevb.47.12224

Related papers

Staggered-field-induced hole pairing in one-dimensional correlated systems

J. Bonča, Peter Prelovšek, Igor Sega +2 more

We examine the influence of a staggered magnetic field on states involving a few holes in the one-dimensional t-J and Hubbard models. We apply exact diagonalizations of small systems, an analytical treatment of an anisotropic model, and a high-field perturbation expansion. Our results suggest that even modest staggered fields, h\ensuremath{\ll}t, induce the formation of bound hole pairs in a broad range of parameters, in particular for J/t1 in the t-J model and for U/t>1 in the Hubbard model. In the same regions, by studying the density-density correlations and the compressibility, we argue that many holes form a paired state and that phase separation does not occur.

Physical Review Letters•Jul 20, 1992•16 citations

Hole pairs in the one-dimensional Hubbard model in a staggered field

Janez Jaklič, Peter Prelovšek

The one-dimensional Hubbard model in a staggered magnetic field h, introduced recently to simulate planar correlated electronic systems, is studied within the unrestricted Hartree-Fock approximation. The emphasis is on solutions for a few holes added to the reference antiferromagnet. Both analytical results, available at U,ht, and numerical results confirm the polaronic character of a single-hole state for all U,h, while bipolarons (bound pairs of holes) are stable for 0U${\mathit{U}}_{\mathit{c}}$(h). Since under the same conditions we do not find any evidence for stable hole clusters and the phase separation, the latter regime remains a candidate for hole pairing.

Physical review. B, Condensed matter•Mar 1, 1993•5 citations

Small-cluster calculations for the simple and extended Hubbard models

J. Callaway, D. P. Chen, D. G. Kanhere +1 more

The single-band Hubbard model (both with and without first-neighbor interactions) is studied by exact diagonalization on several one- and two-dimensional clusters, ranging from four to nine sites, including rings and arrangements of squares. Occupancies include the half-filled band (one electron per site) and configurations with one and two holes in the half-filled band. Ground-state properties are determined for a wide range of parameters. We discuss the phase diagram in the (U,V) plane and consider spin, charge, and pairing correlations. The binding of a pair of holes is investigated. Circumstances in which binding and pairing are enhanced by first-neighbor interactions are described.

Physical review. B, Condensed matter•Jul 1, 1990•41 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

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

Generalized one-dimensionalt-Jmodels with longer-range spin exchange

J. Bonča, Peter Prelovšek

The behavior of holes in the one-dimensional (1D) t-J model differs substantially from the one in planar correlated systems. We show that within the 1D model one can recover some essential properties of 2D systems by including longer-range spin exchange. Be means of analytical calculations for the anisotropic exchange and the exact diagonalization of small systems, it is established that this generalization leads to the large mass enhancement for a single hole, to the hole binding at strongly reduced J/t, and to substantial changes in the phase diagram at electron densities n\ensuremath{\lesssim}1. It is shown that the longer spin exchange changes qualitatively the phase-separation line ${\mathit{J}}_{\mathit{c}}$(n), which obtains an n dependence analogous to the 2D systems, i.e., opposite to the one in the 1D t-J model. The correlation exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ calculated in the Luttinger-liquid regime J${\mathit{J}}_{\mathit{c}}$(n) indicates also that the region of dominant pairing correlations can move even to J/t1.

Physical review. B, Condensed matter•Sep 1, 1992•2 citations
The influence of the staggered magnetic field h on properties of the one-dimensional t-J and Hubbard models with nearly half-filled bands are studied. Using the exact diagonalization method for small systems as well as analytical approaches possible in the anisotropic model and for h\ensuremath{\gg}t, we determine the phase diagram of the t-J-h model at low doping, which displays three different regimes: the phase with repelling holes for JJc{\mathit{J}}_{\mathit{c}}Jc​, the phase with paired holes for Jc{\mathit{J}}_{\mathit{c}}Jc​JJs{\mathit{J}}_{\mathit{s}}Js​, and the phase separation for J>Js{\mathit{J}}_{\mathit{s}}Js​. Employing for h\ensuremath{\ne}0 the analogy with the universal behavior of one-dimensional interacting fermions within the Luther-Emery regime, we calculate the charge exponent K\ensuremathρ{\mathit{K}}_{\mathrm{\ensuremath{\rho}}}K\ensuremathρ​, which can be K\ensuremathρ{\mathit{K}}_{\mathrm{\ensuremath{\rho}}}K\ensuremathρ​>1 in the pairing regime, indicating dominant superconducting fluctuations. An analogous analysis, in particular the perturbation expansion in t/h, performed for the Hubbard t-U-h model shows a phase of stable hole pairs for UUc{\mathit{U}}_{\mathit{c}}Uc​. Again K\ensuremathρ{\mathit{K}}_{\mathrm{\ensuremath{\rho}}}K\ensuremathρ​ seems to approach a nonuniversal value at half-filling.
We examine the influence of a staggered magnetic field on states involving a few holes in the one-dimensional t-J and Hubbard models. We apply exact diagonalizations of small systems, an analytical treatment of an anisotropic model, and a high-field perturbation expansion. Our results suggest that even modest staggered fields, h\ensuremath{\ll}t, induce the formation of bound hole pairs in a broad range of parameters, in particular for J/t1 in the t-J model and for U/t>1 in the Hubbard model. In the same regions, by studying the density-density correlations and the compressibility, we argue that many holes form a paired state and that phase separation does not occur.
The one-dimensional Hubbard model in a staggered magnetic field h, introduced recently to simulate planar correlated electronic systems, is studied within the unrestricted Hartree-Fock approximation. The emphasis is on solutions for a few holes added to the reference antiferromagnet. Both analytical results, available at U,ht, and numerical results confirm the polaronic character of a single-hole state for all U,h, while bipolarons (bound pairs of holes) are stable for 0UUc{\mathit{U}}_{\mathit{c}}Uc​(h). Since under the same conditions we do not find any evidence for stable hole clusters and the phase separation, the latter regime remains a candidate for hole pairing.
The single-band Hubbard model (both with and without first-neighbor interactions) is studied by exact diagonalization on several one- and two-dimensional clusters, ranging from four to nine sites, including rings and arrangements of squares. Occupancies include the half-filled band (one electron per site) and configurations with one and two holes in the half-filled band. Ground-state properties are determined for a wide range of parameters. We discuss the phase diagram in the (U,V) plane and consider spin, charge, and pairing correlations. The binding of a pair of holes is investigated. Circumstances in which binding and pairing are enhanced by first-neighbor interactions are described.
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.
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.
The behavior of holes in the one-dimensional (1D) t-J model differs substantially from the one in planar correlated systems. We show that within the 1D model one can recover some essential properties of 2D systems by including longer-range spin exchange. Be means of analytical calculations for the anisotropic exchange and the exact diagonalization of small systems, it is established that this generalization leads to the large mass enhancement for a single hole, to the hole binding at strongly reduced J/t, and to substantial changes in the phase diagram at electron densities n\ensuremath{\lesssim}1. It is shown that the longer spin exchange changes qualitatively the phase-separation line Jc{\mathit{J}}_{\mathit{c}}Jc​(n), which obtains an n dependence analogous to the 2D systems, i.e., opposite to the one in the 1D t-J model. The correlation exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ calculated in the Luttinger-liquid regime JJc{\mathit{J}}_{\mathit{c}}Jc​(n) indicates also that the region of dominant pairing correlations can move even to J/t1.