arXiv:cond-mat/0306424 · Physical Review Letters

Low-Energy Spectra in t−J -Type Models at Low Doping Levels

Wei-Cheng Lee, T. K. Lee, Chang-Ming Ho, P. W. Leung

Published Jul 29, 2003• 13 citations

Abstract

Based on a variational approach, we propose that there are two kinds of low-energy states in the t-J-type models at low doping. In a quasiparticle state an unpaired spin bound to a hole with a well-defined momentum can be excited with spin waves. The resulting state shows a suppression of antiferromagnetic order around the hole with the profile of a spin bag. These spin-bag states with spin and charge or hole separated form a continuum of low-energy excitations. Very different properties predicted by these two kinds of states explain a number of anomalous results observed in the exact diagonalization studies on small clusters up to 32 sites.

DOI: 10.1103/physrevlett.91.057001

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arXiv:cond-mat/0306424 · Physical Review Letters

Low-Energy Spectra in t−J -Type Models at Low Doping Levels

Wei-Cheng Lee, T. K. Lee, Chang-Ming Ho, P. W. Leung

Published Jul 29, 2003• 13 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.91.057001

Related papers

Anomalous Spin and Charge Dynamics of the t - J Model at Low Doping

R. Eder, Y. Ohta, Sadamichi Maekawa

We present an exact diagonalization study of the dynamical spin and density correlation functions in small clusters of 2D $t\ensuremath{-}J$ model for hole dopings $\ensuremath{\le}25$%. Both correlation functions show a remarkably regular, but very different, scaling with both hole density ${\ensuremath{\rho}}_{h}$ and parameters $t$ and $J$ . The density correlation function is most consistent with that of condensed bosons in a band of width $\ensuremath{\sim}t$, the spin correlation function with that of fermions in a band of width $\ensuremath{\sim}J$. We show that the familiar spin bag scenario explains these results in a natural way.We present an exact diagonalization study of the dynamical spin and density correlation functions in small clusters of 2D $t\ensuremath{-}J$ model for hole dopings $\ensuremath{\le}25$%. Both correlation functions show a remarkably regular, but very different, scaling with both hole density ${\ensuremath{\rho}}_{h}$ and parameters $t$ and $J$. The density correlation function is most consistent with that of condensed bosons in a band of width $\ensuremath{\sim}t$, the spin correlation function with that of fermions in a band of width $\ensuremath{\sim}J$. We show that the familiar spin bag scenario explains these results in a natural way.

arXiv:cond-mat/9501009Physical Review LettersJun 19, 199550 citations

Spin bags in the dopedt-Jmodel

R. Eder, Y. Ohta

We present a nonperturbative method for deriving a quasiparticle description of the low-energy excitations in the t-J model for strongly correlated electrons. Using the exact diagonalization technique we evaluated exactly the spectral functions of composite operators, which describe an electron or hole dressed by antiferromagnetic spin fluctuations as expected in the string or spin bag picture. For hole doping up to 1/8, use of the composite operators leads to a drastic simplification of the single-particle spectral function: at half-filling it takes free-particle form, for the doped case it resembles a system of weakly interacting fermions corresponding to the doped holes. We conclude that for all doping levels studied, the elementary electronic excitations next to the Fermi level are adequately described by the antiferromagnetic spin-fluctuation picture.We present a nonperturbative method for deriving a quasiparticle description of the low-energy excitations in the t-J model for strongly correlated electrons. Using the exact diagonalization technique we evaluated exactly the spectral functions of composite operators, which describe an electron or hole dressed by antiferromagnetic spin fluctuations as expected in the string or spin bag picture. For hole doping up to 1/8, use of the composite operators leads to a drastic simplification of the single-particle spectral function: at half-filling it takes free-particle form, for the doped case it resembles a system of weakly interacting fermions corresponding to the doped holes. We conclude that for all doping levels studied, the elementary electronic excitations next to the Fermi level are adequately described by the antiferromagnetic spin-fluctuation picture.

arXiv:cond-mat/9406098Physical review. B, Condensed matterOct 1, 199420 citations

Hole correlation and antiferromagnetic order in the t−J model

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We study the $t\text{\ensuremath{-}}J$ model with four holes on a 32-site square lattice using exact diagonalization. This system corresponds to doping level $x=\frac{1}{8}$ . At the ``realistic'' parameter $J∕t=0.3$ , holes in the ground state of this system are unbound. They have short range repulsion due to the lowering of the kinetic energy. There is no antiferromagnetic spin order and the electron momentum distribution function resembles hole pockets. Furthermore, we show evidence that in case antiferromagnetic order exists, holes form $d$ -wave bound pairs and there is mutual repulsion among hole pairs. This presumably will occur at low doping levels. This scenario is compatible with a checkerboard-type charge density state proposed to explain the `` $\frac{1}{8}$ anomaly'' in the lanthanum cuprate family, except that it is the ground state only when the system possesses strong antiferromagnetic order.We study the $t\text{\ensuremath{-}}J$ model with four holes on a 32-site square lattice using exact diagonalization. This system corresponds to doping level $x=\frac{1}{8}$. At the ``realistic'' parameter $J∕t=0.3$, holes in the ground state of this system are unbound. They have short range repulsion due to the lowering of the kinetic energy. There is no antiferromagnetic spin order and the electron momentum distribution function resembles hole pockets. Furthermore, we show evidence that in case antiferromagnetic order exists, holes form $d$-wave bound pairs and there is mutual repulsion among hole pairs. This presumably will occur at low doping levels. This scenario is compatible with a checkerboard-type charge density state proposed to explain the ``$\frac{1}{8}$ anomaly'' in the lanthanum cuprate family, except that it is the ground state only when the system possesses strong antiferromagnetic order.

arXiv:cond-mat/0511568Physical Review BJan 3, 200613 citations

Quasiparticle structure and coherent propagation in thet- Jz - J⊥ model

Junwu Gan, Per Hedegård

Numerical studies, from variational calculation to exact diagonalization, all indicate that the quasiparticle generated by introducing one hole into a two-dimensional quantum antiferromagnet has the same nature as a string state in the t- ${\mathit{J}}_{\mathit{z}}$ model. Based on this observation, we attempt to visualize the quasiparticle formation and subsequent coherent propagation at low energy by studying the generalized t- ${\mathit{J}}_{\mathit{z}}$ -${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ model in which we first diagonalize the t- ${\mathit{J}}_{\mathit{z}}$ model and then perform a degenerate perturbation in ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$. We construct the quasiparticle state and derive an effective Hamiltonian describing the coherent propagation of the quasiparticle and its interaction with the spin wave excitations in the presence of the N\'eel order. We expect that qualitative properties of the quasiparticle remain intact when analytically continuing ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ from the anisotropic ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ ${\mathit{J}}_{\mathit{z}}$ to the isotropic ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$= ${\mathit{J}}_{\mathit{z}}$ limit, despite the fact that the spin wave excitations change from gapful to gapless. Extrapolating to ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$= ${\mathit{J}}_{\mathit{z}}$ , our quasiparticle dispersion and spectral weight compare well with the exact numerical results for small clusters. \textcopyright{} 1996 The American Physical Society.Numerical studies, from variational calculation to exact diagonalization, all indicate that the quasiparticle generated by introducing one hole into a two-dimensional quantum antiferromagnet has the same nature as a string state in the t-${\mathit{J}}_{\mathit{z}}$ model. Based on this observation, we attempt to visualize the quasiparticle formation and subsequent coherent propagation at low energy by studying the generalized t-${\mathit{J}}_{\mathit{z}}$-${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ model in which we first diagonalize the t-${\mathit{J}}_{\mathit{z}}$ model and then perform a degenerate perturbation in ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$. We construct the quasiparticle state and derive an effective Hamiltonian describing the coherent propagation of the quasiparticle and its interaction with the spin wave excitations in the presence of the N\'eel order. We expect that qualitative properties of the quasiparticle remain intact when analytically continuing ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ from the anisotropic ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$${\mathit{J}}_{\mathit{z}}$ to the isotropic ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=${\mathit{J}}_{\mathit{z}}$ limit, despite the fact that the spin wave excitations change from gapful to gapless. Extrapolating to ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=${\mathit{J}}_{\mathit{z}}$, our quasiparticle dispersion and spectral weight compare well with the exact numerical results for small clusters. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9507067Physical review. B, Condensed matterJan 1, 19964 citations

Charge and spin dynamics in a doped quantum antiferromagnet

Yasumasa Hasegawa, Didier Poilblanc

We report a calculation of the dynamics of more than one hole in the t-J model using the Lanczos algorithm. The hole spectral weight develops a large quasiparticle peak that describes two holes in the same momentum state on the pseudo-Fermi-surface with antiparallel spins. We also show that doping leads to a narrowing of the bandwidth of the spin-wave dispersion. A larger number of higher-energy subpeaks in the spectral function (compared to half filling) are observed, although they are not predicted by mean-field theory.We report a calculation of the dynamics of more than one hole in the t-J model using the Lanczos algorithm. The hole spectral weight develops a large quasiparticle peak that describes two holes in the same momentum state on the pseudo-Fermi-surface with antiparallel spins. We also show that doping leads to a narrowing of the bandwidth of the spin-wave dispersion. A larger number of higher-energy subpeaks in the spectral function (compared to half filling) are observed, although they are not predicted by mean-field theory.

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Hole binding in thet-Jmodel

P. Wróbel, R. Eder

We calculated the binding energy of two holes with antiparallel spin in the t-J model using a variational wave function based on the string or spin-bag picture. The symmetry of the bound state is ${\mathit{d}}_{\mathit{x}}^{2}$ - ${\mathit{y}}^{2}$ . Although the size of matrices to be diagonalized is only 3\ifmmode\times\else\texttimes\fi{}3 we could reproduce the results of various extensive numerical calculations with reasonable accuracy. We show that a sizeable contribution of the binding energy is due to the quantum fluctuations in the ground state of the Heisenberg antiferromagnet. In contrast to exact diagonalization results on small clusters in the thermodynamical limit the binding energy decreases rapidly with increasing t/J. A detailed discussion of the various finite-size effects in a small cluster is also included.We calculated the binding energy of two holes with antiparallel spin in the t-J model using a variational wave function based on the string or spin-bag picture. The symmetry of the bound state is ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$. Although the size of matrices to be diagonalized is only 3\ifmmode\times\else\texttimes\fi{}3 we could reproduce the results of various extensive numerical calculations with reasonable accuracy. We show that a sizeable contribution of the binding energy is due to the quantum fluctuations in the ground state of the Heisenberg antiferromagnet. In contrast to exact diagonalization results on small clusters in the thermodynamical limit the binding energy decreases rapidly with increasing t/J. A detailed discussion of the various finite-size effects in a small cluster is also included.

Physical review. B, Condensed matterJan 1, 199416 citations

t

and

J

. The density correlation function is most consistent with that of condensed bosons in a band of width $\ensuremath{\sim}t$, the spin correlation function with that of fermions in a band of width $\ensuremath{\sim}J$. We show that the familiar spin bag scenario explains these results in a natural way.

We study the $t\text{\ensuremath{-}}J$ model with four holes on a 32-site square lattice using exact diagonalization. This system corresponds to doping level

x=\frac{1}{8}

. At the ``realistic'' parameter

J∕t=0.3

, holes in the ground state of this system are unbound. They have short range repulsion due to the lowering of the kinetic energy. There is no antiferromagnetic spin order and the electron momentum distribution function resembles hole pockets. Furthermore, we show evidence that in case antiferromagnetic order exists, holes form

d

-wave bound pairs and there is mutual repulsion among hole pairs. This presumably will occur at low doping levels. This scenario is compatible with a checkerboard-type charge density state proposed to explain the ``

\frac{1}{8}

anomaly'' in the lanthanum cuprate family, except that it is the ground state only when the system possesses strong antiferromagnetic order.

{\mathit{J}}_{\mathit{z}}

model. Based on this observation, we attempt to visualize the quasiparticle formation and subsequent coherent propagation at low energy by studying the generalized t-

{\mathit{J}}_{\mathit{z}}

-${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ model in which we first diagonalize the t-

{\mathit{J}}_{\mathit{z}}

model and then perform a degenerate perturbation in ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$. We construct the quasiparticle state and derive an effective Hamiltonian describing the coherent propagation of the quasiparticle and its interaction with the spin wave excitations in the presence of the N\'eel order. We expect that qualitative properties of the quasiparticle remain intact when analytically continuing ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ from the anisotropic ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$

{\mathit{J}}_{\mathit{z}}

to the isotropic ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=

{\mathit{J}}_{\mathit{z}}

limit, despite the fact that the spin wave excitations change from gapful to gapless. Extrapolating to ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=

{\mathit{J}}_{\mathit{z}}

, our quasiparticle dispersion and spectral weight compare well with the exact numerical results for small clusters. \textcopyright{} 1996 The American Physical Society.

We calculated the binding energy of two holes with antiparallel spin in the t-J model using a variational wave function based on the string or spin-bag picture. The symmetry of the bound state is

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

. Although the size of matrices to be diagonalized is only 3\ifmmode\times\else\texttimes\fi{}3 we could reproduce the results of various extensive numerical calculations with reasonable accuracy. We show that a sizeable contribution of the binding energy is due to the quantum fluctuations in the ground state of the Heisenberg antiferromagnet. In contrast to exact diagonalization results on small clusters in the thermodynamical limit the binding energy decreases rapidly with increasing t/J. A detailed discussion of the various finite-size effects in a small cluster is also included.