arXiv:cond-mat/9304044 · Physical review. B, Condensed matter

d-wave bound state of holes in an antiferromagnet

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

Published May 1, 1994• 45 citations

Abstract

The formation of bound states of holes in an antiferromagnetic spin-1/2 background is studied using numerical techniques applied to the t-J Hamiltonian on clusters with up to 26 sites. An analysis of the binding energy as a function of cluster size suggests that a two-hole bound state is formed for couplings larger than a ``critical'' value J/t${\mathrm{\ensuremath{\Vert}}}_{\mathit{c}}$ The symmetry of the bound state is ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$. We also observed that its ``quasiparticle'' weight ${\mathit{Z}}_{2\mathit{h}}$ (defined in the text), is finite for coupling J/t\ensuremath{\ge}J/t${\mathrm{\ensuremath{\Vert}}}_{\mathit{c}}$. Thus, in the region J/t\ensuremath{\ge}J/t${\mathrm{\ensuremath{\Vert}}}_{\mathit{c}}$ the bound state of two holes behaves like a quasiparticle with charge Q=2e, spin S=0, and ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ internal symmetry. The relation with recent ideas that have suggested the possibility of d-wave pairing in theories of the high-${\mathit{T}}_{\mathit{c}}$ cuprates is briefly discussed.

DOI: 10.1103/physrevb.49.12318

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

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Holes in the t−Jz model: A diagrammatic study

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Hole binding in thet-Jmodel

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Two-Hole Ground State: Dichotomy in Pairing Symmetry

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Binding of holes to magnetic impurities in a strongly correlated system

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Two-hole problem in the t - J model: A canonical transformation approach

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arXiv:cond-mat/9304044 · Physical review. B, Condensed matter

d-wave bound state of holes in an antiferromagnet

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

Published May 1, 1994• 45 citations

arXiv HTML PDF

Abstract

critical'' value J/t${\mathrm{\ensuremath{\Vert}}}_{\mathit{c}}$ The symmetry of the bound state is ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$. We also observed that its

quasiparticle'' weight

{\mathit{Z}}_{2\mathit{h}}

(defined in the text), is finite for coupling J/t\ensuremath{\ge}J/t

{\mathrm{\ensuremath{\Vert}}}_{\mathit{c}}

. Thus, in the region J/t\ensuremath{\ge}J/t

{\mathrm{\ensuremath{\Vert}}}_{\mathit{c}}

the bound state of two holes behaves like a quasiparticle with charge Q=2e, spin S=0, and

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

{\mathit{y}}^{2}

internal symmetry. The relation with recent ideas that have suggested the possibility of d-wave pairing in theories of the high-

{\mathit{T}}_{\mathit{c}}

cuprates is briefly discussed.

DOI: 10.1103/physrevb.49.12318

Related papers

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).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/9303029Physical review. B, Condensed matterAug 1, 199349 citations

Holes in the t−Jz model: A diagrammatic study

A. L. Chernyshev, P. W. Leung

The $t\ensuremath{-}{J}_{z}$ model is the strongly anisotropic limit of the $t\ensuremath{-}J$ model which captures some general properties of doped antiferromagnets (AF's). The absence of spin fluctuations simplifies the analytical treatment of hole motion in an AF background, and allows us to calculate single- and two-hole spectra with a high accuracy using a regular diagram technique combined with a real-space approach. At the same time, numerical studies of this model via exact diagonalization on small clusters show negligible finite-size effects for a number of quantities, thus allowing a direct comparison between analytical and numerical results. Both approaches demonstrate that the holes have a tendency to pair in p- and d-wave channels at realistic values of $t/J.$ Interactions leading to pairing and effects selecting p and d waves are thoroughly investigated. The role of transverse spin fluctuations is considered using perturbation theory. Based on the results of the present study, we discuss the pairing problem in the realistic $t\ensuremath{-}J$-like model. Possible implications for preformed pairs formation and phase separation are drawn.The $t\ensuremath{-}{J}_{z}$ model is the strongly anisotropic limit of the $t\ensuremath{-}J$ model which captures some general properties of doped antiferromagnets (AF's). The absence of spin fluctuations simplifies the analytical treatment of hole motion in an AF background, and allows us to calculate single- and two-hole spectra with a high accuracy using a regular diagram technique combined with a real-space approach. At the same time, numerical studies of this model via exact diagonalization on small clusters show negligible finite-size effects for a number of quantities, thus allowing a direct comparison between analytical and numerical results. Both approaches demonstrate that the holes have a tendency to pair in p- and d-wave channels at realistic values of $t/J.$ Interactions leading to pairing and effects selecting p and d waves are thoroughly investigated. The role of transverse spin fluctuations is considered using perturbation theory. Based on the results of the present study, we discuss the pairing problem in the realistic $t\ensuremath{-}J$-like model. Possible implications for preformed pairs formation and phase separation are drawn.

arXiv:cond-mat/9901114Physical review. B, Condensed matterJul 15, 199966 citations

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

Two-Hole Ground State: Dichotomy in Pairing Symmetry

Jingyu Zhao, Shuai A. Chen, Hao-Kai Zhang +1 more

A single-hole ground state Ansatz for the two-dimensional t-J model has been recently studied by the variational Monte Carlo (VMC) method.Such a doped hole behaves like a "twisted" non-Landau quasiparticle characterized by an emergent quantum number in agreement with exact numerics.In this work, we further investigate the ground state of two holes by VMC.It is found that the two holes strongly attract each other to form a pairing state with a new quantum number the same as obtained by the numerical exact diagonalization and density matrix renormalization group (DMRG) calculations.A unique feature of this pairing state is a dichotomy in the pairing symmetry, i.e., a d wave in terms of the electron c operators and an s wave in terms of the new quasiparticles, as explicitly illustrated in the ground state wave function.A similar VMC study of a two-hole wave function for the t-J two-leg ladder also yields a good agreement with the DMRG result.We demonstrate that the pairing mechanism responsible for the strong binding here is not due to the long-range antiferromagnetic order nor the resonating-valence-bound pairing in the spin background but is the consequence of the quantum phase strings created by the hopping of holes.The resulting spin-current pattern mediating the pairing force is explicitly illustrated in the VMC calculation.Physical implications to superconductivity at finite doping are also discussed.A single-hole ground state Ansatz for the two-dimensional t-J model has been recently studied by the variational Monte Carlo (VMC) method.Such a doped hole behaves like a "twisted" non-Landau quasiparticle characterized by an emergent quantum number in agreement with exact numerics.In this work, we further investigate the ground state of two holes by VMC.It is found that the two holes strongly attract each other to form a pairing state with a new quantum number the same as obtained by the numerical exact diagonalization and density matrix renormalization group (DMRG) calculations.A unique feature of this pairing state is a dichotomy in the pairing symmetry, i.e., a d wave in terms of the electron c operators and an s wave in terms of the new quasiparticles, as explicitly illustrated in the ground state wave function.A similar VMC study of a two-hole wave function for the t-J two-leg ladder also yields a good agreement with the DMRG result.We demonstrate that the pairing mechanism responsible for the strong binding here is not due to the long-range antiferromagnetic order nor the resonating-valence-bound pairing in the spin background but is the consequence of the quantum phase strings created by the hopping of holes.The resulting spin-current pattern mediating the pairing force is explicitly illustrated in the VMC calculation.Physical implications to superconductivity at finite doping are also discussed.

arXiv:2106.14898Physical Review XMar 31, 202223 citations

Binding of holes to magnetic impurities in a strongly correlated system

Didier Poilblanc, Douglas J. Scalapino, Werner R. Hanke

The effect of a magnetic (S=1/2) impurity coupled to a two-dimensional system of correlated electrons (described by the t-J model) is studied by exact diagonalizations. It is found that, if the exchange coupling of the impurity with the neighboring spins is ferromagnetic or weakly antiferromagnetic, an extra hole can form bound states of different spatial symmetries with the impurity extending to a few lattice spacings. The binding energy is maximum when the impurity is completely decoupled (vacancy) and vanishes for an antiferromagnetic coupling exceeding \ensuremath{\sim}0.3J. Several peaks appear in the single-hole spectral function below the lower edge of the quasiparticle band as signatures of the d-, s-, and p-wave bound states.The effect of a magnetic (S=1/2) impurity coupled to a two-dimensional system of correlated electrons (described by the t-J model) is studied by exact diagonalizations. It is found that, if the exchange coupling of the impurity with the neighboring spins is ferromagnetic or weakly antiferromagnetic, an extra hole can form bound states of different spatial symmetries with the impurity extending to a few lattice spacings. The binding energy is maximum when the impurity is completely decoupled (vacancy) and vanishes for an antiferromagnetic coupling exceeding \ensuremath{\sim}0.3J. Several peaks appear in the single-hole spectral function below the lower edge of the quasiparticle band as signatures of the d-, s-, and p-wave bound states.

arXiv:cond-mat/9404092Physical review. B, Condensed matterNov 1, 199427 citations

Two-hole problem in the t - J model: A canonical transformation approach

V. I. Belinicher, A. L. Chernyshev, V. A. Shubin

The $t$ - $J$ model in the spinless-fermion representation is studied. An effective Hamiltonian for the quasiparticles is derived using a canonical transformation approach. It is shown that the rather simple form of the transformation generator allows one to take into account the effect of hole interactions with the short-range spin waves and to describe the single-hole ground state. Obtained results are very close to ones of the self-consistent Born approximation. Further accounting of the long-range spin-wave interaction is possible on a perturbative basis. Spin-wave exchange and an effective interaction due to minimization of the number of broken antiferromagnetic bonds are included in the effective quasiparticle Hamiltonian. The two-hole bound state problem is solved using a Bethe-Salpeter equation. The only bound state found to exist in the region of $1<(t/J)<5$ is the $d$ wave. Both types of the hole-hole interaction are important for its formation. A discussion of the possible relation of the obtained results to the problem of superconductivity in real systems is presented.The $t$-$J$ model in the spinless-fermion representation is studied. An effective Hamiltonian for the quasiparticles is derived using a canonical transformation approach. It is shown that the rather simple form of the transformation generator allows one to take into account the effect of hole interactions with the short-range spin waves and to describe the single-hole ground state. Obtained results are very close to ones of the self-consistent Born approximation. Further accounting of the long-range spin-wave interaction is possible on a perturbative basis. Spin-wave exchange and an effective interaction due to minimization of the number of broken antiferromagnetic bonds are included in the effective quasiparticle Hamiltonian. The two-hole bound state problem is solved using a Bethe-Salpeter equation. The only bound state found to exist in the region of $1<(t/J)<5$ is the $d$ wave. Both types of the hole-hole interaction are important for its formation. A discussion of the possible relation of the obtained results to the problem of superconductivity in real systems is presented.

arXiv:cond-mat/9611001Physical review. B, Condensed matterAug 1, 199754 citations

critical'' value J/t${\mathrm{\ensuremath{\Vert}}}_{\mathit{c}}$ The symmetry of the bound state is ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$. We also observed that its

quasiparticle'' weight

{\mathit{Z}}_{2\mathit{h}}

(defined in the text), is finite for coupling J/t\ensuremath{\ge}J/t

{\mathrm{\ensuremath{\Vert}}}_{\mathit{c}}

. Thus, in the region J/t\ensuremath{\ge}J/t

{\mathrm{\ensuremath{\Vert}}}_{\mathit{c}}

the bound state of two holes behaves like a quasiparticle with charge Q=2e, spin S=0, and

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

{\mathit{y}}^{2}

internal symmetry. The relation with recent ideas that have suggested the possibility of d-wave pairing in theories of the high-

{\mathit{T}}_{\mathit{c}}

cuprates is briefly discussed.

t/J.

Interactions leading to pairing and effects selecting p and d waves are thoroughly investigated. The role of transverse spin fluctuations is considered using perturbation theory. Based on the results of the present study, we discuss the pairing problem in the realistic $t\ensuremath{-}J$-like model. Possible implications for preformed pairs formation and phase separation are drawn.

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.

The

t

J

model in the spinless-fermion representation is studied. An effective Hamiltonian for the quasiparticles is derived using a canonical transformation approach. It is shown that the rather simple form of the transformation generator allows one to take into account the effect of hole interactions with the short-range spin waves and to describe the single-hole ground state. Obtained results are very close to ones of the self-consistent Born approximation. Further accounting of the long-range spin-wave interaction is possible on a perturbative basis. Spin-wave exchange and an effective interaction due to minimization of the number of broken antiferromagnetic bonds are included in the effective quasiparticle Hamiltonian. The two-hole bound state problem is solved using a Bethe-Salpeter equation. The only bound state found to exist in the region of

1<(t/J)<5

is the

d

wave. Both types of the hole-hole interaction are important for its formation. A discussion of the possible relation of the obtained results to the problem of superconductivity in real systems is presented.