Progress of Theoretical Physics Supplement

Dynamics of Two Holes in thet-JModel

Jun-ichiro Inoue, Sadamichi Maekawa

Published Jan 1, 1992• 11 citations

Abstract

Ground state properties of two holes in the antiferromagnetic state in a square lattice are studied by using the t-J model and a variational method where the Hilbert space is restricted. It is shown that two holes are bound to each other and the ground state has d-symmetry for J/∣t∣≳ 0.18 with the momentum K = (0, 0). The binding energy of two holes is -0.7 ∼ -0.5 × J/∣t∣ and the average distance between two holes is 1.6 ∼ 1.8 × a, where a is the lattice constant, for realistic parameter values. Static correlation function Szz(Q) shows a broad peak around Q = (π/2, π/2) which originates from the motion of holes. By making use of the results for one and two holes, an effective Hamiltonian for the quasi-particles is proposed.

DOI: 10.1143/ptps.108.313

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Progress of Theoretical Physics Supplement

Dynamics of Two Holes in thet-JModel

Jun-ichiro Inoue, Sadamichi Maekawa

Published Jan 1, 1992• 11 citations

Publisher

Abstract

DOI: 10.1143/ptps.108.313

Related papers

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

Hole motion in thet-Jand Hubbard models: Effect of a next-nearest-neighbor hopping

Eduardo R. Gagliano, Silvia Bacci, Elbio R. Dagotto

Using exact diagonalization techniques, we study one dynamical hole in the two-dimensional t-J and Hubbard models on a square lattice including a next-nearest-neighbor hopping t'. We present the phase diagram in the parameter space (J/t,t'/t), discussing the ground-state properties of the hole. At J=0, a crossing of levels exists at some value of t' separating a ferromagnetic from an antiferromagnetic ground state. For nonzero J, at least four different regions appear where the system behaves like an antiferromagnet or a (not fully saturated) ferromagnet. We study the quasiparticle behavior of the hole, showing that for small values of \ensuremath{\Vert}t'\ensuremath{\Vert} the previously presented string picture is still valid. We also find that, for a realistic set of parameters derived from the Cu-O Hamiltonian, the hole has momentum (\ensuremath{\pi}/2,\ensuremath{\pi}/2), suggesting an enhancement of the p-wave superconducting mode due to the second-neighbor interactions in the spin-bag picture. Results for the t-t'-U model are also discussed with conclusions similar to those of the t-t'-J model. In general we found that t'=0 is not a singular point of these models.Using exact diagonalization techniques, we study one dynamical hole in the two-dimensional t-J and Hubbard models on a square lattice including a next-nearest-neighbor hopping t'. We present the phase diagram in the parameter space (J/t,t'/t), discussing the ground-state properties of the hole. At J=0, a crossing of levels exists at some value of t' separating a ferromagnetic from an antiferromagnetic ground state. For nonzero J, at least four different regions appear where the system behaves like an antiferromagnet or a (not fully saturated) ferromagnet. We study the quasiparticle behavior of the hole, showing that for small values of \ensuremath{\Vert}t'\ensuremath{\Vert} the previously presented string picture is still valid. We also find that, for a realistic set of parameters derived from the Cu-O Hamiltonian, the hole has momentum (\ensuremath{\pi}/2,\ensuremath{\pi}/2), suggesting an enhancement of the p-wave superconducting mode due to the second-neighbor interactions in the spin-bag picture. Results for the t-t'-U model are also discussed with conclusions similar to those of the t-t'-J model. In general we found that t'=0 is not a singular point of these models.

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Fabio Mezzacapo, Adriano Angelone, Guido Pupillo

We show that the entangled-plaquette variational Ansatz can be adapted to study the two-dimensional t-J model in the presence of two mobile holes. Specifically, we focus on a square lattice comprising up to $N=256$ sites in the parameter range $0.4\ensuremath{\le}J/t\ensuremath{\le}2.0$. Ground state energies are obtained via the optimization of a wave function in which the weight of a given configuration is expressed in terms of variational coefficients associated with square and linear entangled plaquettes. Our estimates are in excellent agreement with exact results available for the $N=16$ lattice. By extending our study to considerably larger systems we find, based on the analysis of the long-distance tail of the probability of finding two holes at spatial separation $r$ , and on our computed two-hole binding energies, the existence of a two-hole bound state for all the values of $J/t$ explored here. It is estimated that $d$ -wave binding of the two holes does not occur for $J/t<{J}_{c}/t\ensuremath{\simeq}0.19$.We show that the entangled-plaquette variational Ansatz can be adapted to study the two-dimensional t-J model in the presence of two mobile holes. Specifically, we focus on a square lattice comprising up to $N=256$ sites in the parameter range $0.4\ensuremath{\le}J/t\ensuremath{\le}2.0$. Ground state energies are obtained via the optimization of a wave function in which the weight of a given configuration is expressed in terms of variational coefficients associated with square and linear entangled plaquettes. Our estimates are in excellent agreement with exact results available for the $N=16$ lattice. By extending our study to considerably larger systems we find, based on the analysis of the long-distance tail of the probability of finding two holes at spatial separation $r$, and on our computed two-hole binding energies, the existence of a two-hole bound state for all the values of $J/t$ explored here. It is estimated that $d$-wave binding of the two holes does not occur for $J/t<{J}_{c}/t\ensuremath{\simeq}0.19$.

arXiv:1610.04205Physical review. B./Physical review. BOct 13, 201610 citations

Dynamical pair susceptibilities in thet-Jand Hubbard models

Elbio R. Dagotto, José A. Riera, A. P. Young

We study dynamical properties of two holes in the t-J, t- ${\mathit{J}}_{\mathit{z}}$ , and Hubbard models using exact diagonalization techniques on small clusters. For the three models we found that the ground state of two holes has d-wave symmetry. Studying the dynamical d-wave pairing susceptibility at zero momentum, we observed a quasiparticle-like peak at the bottom of the spectrum in a broad region of parameter space. The lowest-energy p-wave state is close in energy to the d-wave ground state, and they both behave qualitatively similarly, while the lowest-energy states of the s-wave and extended-s-wave subspaces have higher energies and present no quasiparticle peak. The ground-state energy of two holes in the t-J model scales with J as a power law. Binding energies for different symmetries as well as dynamical properties for nonzero momentum are also discussed.We study dynamical properties of two holes in the t-J, t-${\mathit{J}}_{\mathit{z}}$, and Hubbard models using exact diagonalization techniques on small clusters. For the three models we found that the ground state of two holes has d-wave symmetry. Studying the dynamical d-wave pairing susceptibility at zero momentum, we observed a quasiparticle-like peak at the bottom of the spectrum in a broad region of parameter space. The lowest-energy p-wave state is close in energy to the d-wave ground state, and they both behave qualitatively similarly, while the lowest-energy states of the s-wave and extended-s-wave subspaces have higher energies and present no quasiparticle peak. The ground-state energy of two holes in the t-J model scales with J as a power law. Binding energies for different symmetries as well as dynamical properties for nonzero momentum are also discussed.

Physical review. B, Condensed matterAug 1, 199070 citations

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 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.

N=256

sites in the parameter range $0.4\ensuremath{\le}J/t\ensuremath{\le}2.0$. Ground state energies are obtained via the optimization of a wave function in which the weight of a given configuration is expressed in terms of variational coefficients associated with square and linear entangled plaquettes. Our estimates are in excellent agreement with exact results available for the

N=16

lattice. By extending our study to considerably larger systems we find, based on the analysis of the long-distance tail of the probability of finding two holes at spatial separation

r

, and on our computed two-hole binding energies, the existence of a two-hole bound state for all the values of

J/t

explored here. It is estimated that

d

-wave binding of the two holes does not occur for $J/t<{J}_{c}/t\ensuremath{\simeq}0.19$.

We study dynamical properties of two holes in the t-J, t-

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

, and Hubbard models using exact diagonalization techniques on small clusters. For the three models we found that the ground state of two holes has d-wave symmetry. Studying the dynamical d-wave pairing susceptibility at zero momentum, we observed a quasiparticle-like peak at the bottom of the spectrum in a broad region of parameter space. The lowest-energy p-wave state is close in energy to the d-wave ground state, and they both behave qualitatively similarly, while the lowest-energy states of the s-wave and extended-s-wave subspaces have higher energies and present no quasiparticle peak. The ground-state energy of two holes in the t-J model scales with J as a power law. Binding energies for different symmetries as well as dynamical properties for nonzero momentum are also discussed.