Physical review. B, Condensed matter

Hole binding in thet-Jmodel

P. Wróbel, R. Eder

Published Jan 1, 1994• 16 citations

Abstract

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.

DOI: 10.1103/physrevb.49.1233

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

Didier Poilblanc

arXiv:cond-mat/9303029Physical review. B, Condensed matterAug 1, 199349 citations

Two-holed-wave binding in the physical region of thet-Jmodel: A Green’s-function Monte Carlo study

Massimo Boninsegni, Efstratios Manousakis

Physical review. B, Condensed matterMay 1, 199360 citations

Hole dynamics in thet-Jmodel: An exact diagonalization study

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Single hole in a quantum antiferromagnet: Finite-size-scaling approach

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Physical review. B, Condensed matterSep 1, 199235 citations

Interaction of quasiparticles in thet-Jmodel

R. Eder

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Dynamical properties of a hole in a Heisenberg antiferromagnet

Zhiping Liu, Efstratios Manousakis

Physical review. B, Condensed matterFeb 1, 1992274 citations

Physical review. B, Condensed matter

Hole binding in thet-Jmodel

P. Wróbel, R. Eder

Published Jan 1, 1994• 16 citations

Publisher

Abstract

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.

DOI: 10.1103/physrevb.49.1233

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

Two-holed-wave binding in the physical region of thet-Jmodel: A Green’s-function Monte Carlo study

Massimo Boninsegni, Efstratios Manousakis

We investigate numerically the ground state of two holes with ${\mathit{d}}_{\mathit{x}}^{2}$ - ${\mathit{y}}^{2}$ symmetry in the two-dimensional t-J model, on lattices of significantly larger sizes than the ones studied so far. The Green's-function Monte Carlo method, in conjunction with suitable initial states and guidance functions, is used to estimate the ground-state energy of one and two holes, as well as to compute the two-hole distribution function. Our results show a significant decrease of the two-hole binding energy as the size of the lattice is increased from 4\ifmmode\times\else\texttimes\fi{}4. A critical value ${\mathit{J}}_{\mathit{c}}$ \ensuremath{\sim}0.27t is found such that d-wave hole binding no longer occurs for J ${\mathit{J}}_{\mathit{c}}$ .We investigate numerically the ground state of two holes with ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ symmetry in the two-dimensional t-J model, on lattices of significantly larger sizes than the ones studied so far. The Green's-function Monte Carlo method, in conjunction with suitable initial states and guidance functions, is used to estimate the ground-state energy of one and two holes, as well as to compute the two-hole distribution function. Our results show a significant decrease of the two-hole binding energy as the size of the lattice is increased from 4\ifmmode\times\else\texttimes\fi{}4. A critical value ${\mathit{J}}_{\mathit{c}}$\ensuremath{\sim}0.27t is found such that d-wave hole binding no longer occurs for J${\mathit{J}}_{\mathit{c}}$.

Physical review. B, Condensed matterMay 1, 199360 citations

Hole dynamics in thet-Jmodel: An exact diagonalization study

Yukio Hasegawa, Didier Poilblanc

Exact many-body states of square clusters up to 18 sites (with periodic boundary conditions) are investigated in order to study the dynamics of one or two holes in the t-J model. Our method takes full advantage of the translation, rotation, and reflection symmetries of the cluster. Using a modified Lanczos algorithm, we calculate the lowest state of all the different space-group representations and its total spin as well as its spin and hole correlations. For a single hole, at intermediate J/t values, the magnetic, kinetic energies, and staggered magnetization follow J/t power-law behaviors with size-dependent exponents. A binding energy of order J between two holes appears for sufficiently large J/t(\ensuremath{\ge}0.25). One-hole and two-hole calculations give different results regarding the stability of the Nagaoka state (against the singlet state) when J/t\ensuremath{\rightarrow}0. Energy expectation values of variational resonating-valence-bond states are calculated exactly and optimized. Significant overlaps with the exact states are found for any symmetry.Exact many-body states of square clusters up to 18 sites (with periodic boundary conditions) are investigated in order to study the dynamics of one or two holes in the t-J model. Our method takes full advantage of the translation, rotation, and reflection symmetries of the cluster. Using a modified Lanczos algorithm, we calculate the lowest state of all the different space-group representations and its total spin as well as its spin and hole correlations. For a single hole, at intermediate J/t values, the magnetic, kinetic energies, and staggered magnetization follow J/t power-law behaviors with size-dependent exponents. A binding energy of order J between two holes appears for sufficiently large J/t(\ensuremath{\ge}0.25). One-hole and two-hole calculations give different results regarding the stability of the Nagaoka state (against the singlet state) when J/t\ensuremath{\rightarrow}0. Energy expectation values of variational resonating-valence-bond states are calculated exactly and optimized. Significant overlaps with the exact states are found for any symmetry.

Physical review. B, Condensed matterNov 1, 1989169 citations

Single hole in a quantum antiferromagnet: Finite-size-scaling approach

Didier Poilblanc, Heinz J. Schulz, Timothy A. L. Ziman

Exact diagonalizations of small clusters up to 26 sites are used to extrapolate the ground-state energy of a single hole in the N\'eel state of the t- ${\mathit{J}}_{\mathit{z}}$ model or in the quantum antiferromagnetic (t-J model). A surprisingly rapid convergence with system size is observed for a wide range of parameters and for the largest clusters considered. In the Ising limit the energy dependence with ${\mathit{J}}_{\mathit{z}}$ is remarkably close to a ${\mathit{J}}_{\mathit{z}}^{2/3}$ law for intermediate coupling in agreement with Brinkman-Rice type of calculations. Nevertheless a small but significant bandwidth indicates that the hole can propagate coherently in this limit. Clearly the polaronic behavior \ensuremath{\sim} ${\mathit{J}}_{\mathit{z}}^{1/2}$ , for very small ${\mathit{J}}_{\mathit{z}}$ , is out of the range of the method. When quantum fluctuations are introduced (isotropic case) the ground-state energy behavior still remains close to that of the Ising limit although an overall increase of the energy by a factor 0.3t is observed. This suggests that the ``string scenario'' might have some relevance there.Exact diagonalizations of small clusters up to 26 sites are used to extrapolate the ground-state energy of a single hole in the N\'eel state of the t-${\mathit{J}}_{\mathit{z}}$ model or in the quantum antiferromagnetic (t-J model). A surprisingly rapid convergence with system size is observed for a wide range of parameters and for the largest clusters considered. In the Ising limit the energy dependence with ${\mathit{J}}_{\mathit{z}}$ is remarkably close to a ${\mathit{J}}_{\mathit{z}}^{2/3}$ law for intermediate coupling in agreement with Brinkman-Rice type of calculations. Nevertheless a small but significant bandwidth indicates that the hole can propagate coherently in this limit. Clearly the polaronic behavior \ensuremath{\sim}${\mathit{J}}_{\mathit{z}}^{1/2}$, for very small ${\mathit{J}}_{\mathit{z}}$, is out of the range of the method. When quantum fluctuations are introduced (isotropic case) the ground-state energy behavior still remains close to that of the Ising limit although an overall increase of the energy by a factor 0.3t is observed. This suggests that the ``string scenario'' might have some relevance there.

Physical review. B, Condensed matterSep 1, 199235 citations

Interaction of quasiparticles in thet-Jmodel

R. Eder

The ground state of two holes with opposite spins in the t-J model is discussed using a variational method in a restricted Hilbert space. It is assumed that the holes can move independently and scatter when they are close to each other. Various processes which lead to a scattering of the holes are all treated on the same footing. It is found that the two holes form a bound state with a binding energy which is smaller than 0.4J for any value t/J. A possible extension to the case of finite concentrations is discussed.The ground state of two holes with opposite spins in the t-J model is discussed using a variational method in a restricted Hilbert space. It is assumed that the holes can move independently and scatter when they are close to each other. Various processes which lead to a scattering of the holes are all treated on the same footing. It is found that the two holes form a bound state with a binding energy which is smaller than 0.4J for any value t/J. A possible extension to the case of finite concentrations is discussed.

Physical review. B, Condensed matterJan 1, 199245 citations

Dynamical properties of a hole in a Heisenberg antiferromagnet

Zhiping Liu, Efstratios Manousakis

The t-J model in the large-t/J and low-doping limit is approximated by an effective Hamiltonian that treats spin degrees of freedom within the linear-spin-wave approximation and the hole-hopping term with a hole-spin interaction vertex that is linear in the spin-wave operators. The Dyson's equation for the single-hole Green's function is solved numerically on finite- but sufficiently large-size square lattices. Our calculation is based on an approximate equation for the hole motion that has been obtained using a self-consistent perturbation approach where crossing diagrams are neglected. We have studied the contribution of vertex corrections and found that the leading two-loop crossing diagram is exactly zero. Thus, the leading nonzero contribution to the proper self-energy from crossing diagrams is a three-loop correction. In two dimensions, it is possible to solve Dyson's equation numerically including these three-loop corrections. The results demonstrate that the contribution of such vertex corrections is indeed small. Our solution for the hole spectral function, obtained by neglecting such small contributions from vertex corrections, shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the ${4}^{2}$ lattice in the region of J/t\ensuremath{\le}0.2. The results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function remain while others change due to finite-size effects. In particular, we find well-defined peaks above the lowest-energy peak that survive in the thermodynamic limit. We analyze these higher-energy peaks of the spectral functions and find that they can be understood as ``string'' excitations, which are created by the hole moving in a nearly linear potential.The t-J model in the large-t/J and low-doping limit is approximated by an effective Hamiltonian that treats spin degrees of freedom within the linear-spin-wave approximation and the hole-hopping term with a hole-spin interaction vertex that is linear in the spin-wave operators. The Dyson's equation for the single-hole Green's function is solved numerically on finite- but sufficiently large-size square lattices. Our calculation is based on an approximate equation for the hole motion that has been obtained using a self-consistent perturbation approach where crossing diagrams are neglected. We have studied the contribution of vertex corrections and found that the leading two-loop crossing diagram is exactly zero. Thus, the leading nonzero contribution to the proper self-energy from crossing diagrams is a three-loop correction. In two dimensions, it is possible to solve Dyson's equation numerically including these three-loop corrections. The results demonstrate that the contribution of such vertex corrections is indeed small. Our solution for the hole spectral function, obtained by neglecting such small contributions from vertex corrections, shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the ${4}^{2}$ lattice in the region of J/t\ensuremath{\le}0.2. The results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function remain while others change due to finite-size effects. In particular, we find well-defined peaks above the lowest-energy peak that survive in the thermodynamic limit. We analyze these higher-energy peaks of the spectral functions and find that they can be understood as ``string'' excitations, which are created by the hole moving in a nearly linear potential.

Physical review. B, Condensed matterFeb 1, 1992274 citations

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}

We investigate numerically the ground state of two holes with

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

{\mathit{y}}^{2}

symmetry in the two-dimensional t-J model, on lattices of significantly larger sizes than the ones studied so far. The Green's-function Monte Carlo method, in conjunction with suitable initial states and guidance functions, is used to estimate the ground-state energy of one and two holes, as well as to compute the two-hole distribution function. Our results show a significant decrease of the two-hole binding energy as the size of the lattice is increased from 4\ifmmode\times\else\texttimes\fi{}4. A critical value

{\mathit{J}}_{\mathit{c}}

\ensuremath{\sim}0.27t is found such that d-wave hole binding no longer occurs for J

{\mathit{J}}_{\mathit{c}}

Exact diagonalizations of small clusters up to 26 sites are used to extrapolate the ground-state energy of a single hole in the N\'eel state of the t-

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

model or in the quantum antiferromagnetic (t-J model). A surprisingly rapid convergence with system size is observed for a wide range of parameters and for the largest clusters considered. In the Ising limit the energy dependence with

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

is remarkably close to a

{\mathit{J}}_{\mathit{z}}^{2/3}

law for intermediate coupling in agreement with Brinkman-Rice type of calculations. Nevertheless a small but significant bandwidth indicates that the hole can propagate coherently in this limit. Clearly the polaronic behavior \ensuremath{\sim}

{\mathit{J}}_{\mathit{z}}^{1/2}

, for very small

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

, is out of the range of the method. When quantum fluctuations are introduced (isotropic case) the ground-state energy behavior still remains close to that of the Ising limit although an overall increase of the energy by a factor 0.3t is observed. This suggests that the ``string scenario'' might have some relevance there.

{4}^{2}

lattice in the region of J/t\ensuremath{\le}0.2. The results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function remain while others change due to finite-size effects. In particular, we find well-defined peaks above the lowest-energy peak that survive in the thermodynamic limit. We analyze these higher-energy peaks of the spectral functions and find that they can be understood as ``string'' excitations, which are created by the hole moving in a nearly linear potential.