Physical review. B, Condensed matter

Renormalization of the hole–spin-wave coupling constant in thet-Jmodel

Oleg P. Sushkov

Published Jan 1, 1994• 32 citations

Abstract

We consider the properties of the holes on an antiferromagnetic background in the two-dimensional t-J model. The long-range dynamics of the system is defined by the interaction of a hole with spin-wave excitations. In the present work the renormalized coupling constant of this interaction f(t) is calculated. For small t, f(t)\ensuremath{\approxeq}3.4t. For large t the coupling constant is t independent, f(t)\ensuremath{\approxeq}2J.

DOI: 10.1103/physrevb.49.1250

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

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Physical review. B, Condensed matter

Renormalization of the hole–spin-wave coupling constant in thet-Jmodel

Oleg P. Sushkov

Published Jan 1, 1994• 32 citations

Publisher

Abstract

DOI: 10.1103/physrevb.49.1250

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

Dynamics of a small density of holes in a two-dimensional quantum antiferromagnet

Bumsoo Kyung, Sergei I. Mukhin

The hole dynamics in a quantum antiferromagnetic background for a small doping concentration is studied within the t-J model description. The noncrossing approximation for the hole self-energy is used. The correct quasiparticle pole structure (without artificial broadening) in the spectral density function is employed. Dyson's equation for the hole Green's function is solved numerically by introducing a lattice in momentum space. The evolution of the density of states and the momentum-distribution function for holes is investigated as a function of hole-magnon coupling constant t at fixed J. The momentum distribution function shows a sharp drop at the Fermi surface for several different hole-magnon coupling constants. This indicates the validity of the Fermi liquid description for the t-J model in the low doping concentration. The volume (surface) enclosed by the Fermi surface (curve) is found to be invariant for all the coupling strengths we have studied. The incoherent spectrum below the chemical potential in the density of states becomes more significant for stronger interaction constants. These features numerically verify Luttinger's theorem for a small density of doped holes in the t-J model. The optical conductivity is computed using the lowest-order diagrams. As the hole-magnon coupling constant t increases, absorption becomes stronger at \ensuremath{\omega}\ensuremath{\simeq}2J, the characteristic frequency for spin waves. This feature may be associated with the experimentally observed midinfrared absorption band in underdoped cuprates.The hole dynamics in a quantum antiferromagnetic background for a small doping concentration is studied within the t-J model description. The noncrossing approximation for the hole self-energy is used. The correct quasiparticle pole structure (without artificial broadening) in the spectral density function is employed. Dyson's equation for the hole Green's function is solved numerically by introducing a lattice in momentum space. The evolution of the density of states and the momentum-distribution function for holes is investigated as a function of hole-magnon coupling constant t at fixed J. The momentum distribution function shows a sharp drop at the Fermi surface for several different hole-magnon coupling constants. This indicates the validity of the Fermi liquid description for the t-J model in the low doping concentration. The volume (surface) enclosed by the Fermi surface (curve) is found to be invariant for all the coupling strengths we have studied. The incoherent spectrum below the chemical potential in the density of states becomes more significant for stronger interaction constants. These features numerically verify Luttinger's theorem for a small density of doped holes in the t-J model. The optical conductivity is computed using the lowest-order diagrams. As the hole-magnon coupling constant t increases, absorption becomes stronger at \ensuremath{\omega}\ensuremath{\simeq}2J, the characteristic frequency for spin waves. This feature may be associated with the experimentally observed midinfrared absorption band in underdoped cuprates.

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Dynamics of a hole in thet-Jmodel with local disorder: Exact results for high dimensions

Rainer Strack, D. Vollhardt

We investigate the t-J model including local disorder for a hole in an antiferromagnetic spin background on a hypercubic lattice in d dimensions. We show that the well-known approximation of a linear potential, caused by the Ising term of the spin-spin interaction, is correct up to order 1/ ${\mathit{d}}^{2}$ and hence becomes exact in d=\ensuremath{\infty}. We also investigate the influence of disorder and compute exactly the Green function and the density of states for a hole in an antiferromagnetic spin background for arbitrary disorder and J in the limit d\ensuremath{\rightarrow}\ensuremath{\infty}. Moreover, for finite J and disorder we determine the dynamical conductivity in high dimensions exactly. Remarkable structure both in the density of states and in the dynamical conductivity is found. Finally, we systematically derive the retraceable path approximation by Brinkman and Rice via a self-consistent 1/d expansion, which is correct up to order 1/ ${\mathit{d}}^{4}$ .We investigate the t-J model including local disorder for a hole in an antiferromagnetic spin background on a hypercubic lattice in d dimensions. We show that the well-known approximation of a linear potential, caused by the Ising term of the spin-spin interaction, is correct up to order 1/${\mathit{d}}^{2}$ and hence becomes exact in d=\ensuremath{\infty}. We also investigate the influence of disorder and compute exactly the Green function and the density of states for a hole in an antiferromagnetic spin background for arbitrary disorder and J in the limit d\ensuremath{\rightarrow}\ensuremath{\infty}. Moreover, for finite J and disorder we determine the dynamical conductivity in high dimensions exactly. Remarkable structure both in the density of states and in the dynamical conductivity is found. Finally, we systematically derive the retraceable path approximation by Brinkman and Rice via a self-consistent 1/d expansion, which is correct up to order 1/${\mathit{d}}^{4}$.

Physical review. B, Condensed matterDec 1, 199250 citations

Dynamics of Two Holes in thet-JModel

Jun-ichiro Inoue, Sadamichi Maekawa

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.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.

Progress of Theoretical Physics SupplementJan 1, 199211 citations

Spin polarons in thet-Jmodel: Shape and backflow

A. Ramšak, Peter Horsch

The self-consistent Born approximation for the self-energy and the wave function of a single hole moving in a two-dimensional quantum antiferromagnet is used to calculate various spin-correlation functions that characterize the perturbation induced by the hole. The results for these correlation functions agree with the available small-cluster calculations. The hole-spin correlation functions decay asymptotically with the distance from the hole as a power law and exhibit a dipolar distortion of the antiferromagnet. The quasiparticle spectral weight remains finite.The self-consistent Born approximation for the self-energy and the wave function of a single hole moving in a two-dimensional quantum antiferromagnet is used to calculate various spin-correlation functions that characterize the perturbation induced by the hole. The results for these correlation functions agree with the available small-cluster calculations. The hole-spin correlation functions decay asymptotically with the distance from the hole as a power law and exhibit a dipolar distortion of the antiferromagnet. The quasiparticle spectral weight remains finite.

Physical review. B, Condensed matterOct 1, 199352 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

{\mathit{d}}^{2}

and hence becomes exact in d=\ensuremath{\infty}. We also investigate the influence of disorder and compute exactly the Green function and the density of states for a hole in an antiferromagnetic spin background for arbitrary disorder and J in the limit d\ensuremath{\rightarrow}\ensuremath{\infty}. Moreover, for finite J and disorder we determine the dynamical conductivity in high dimensions exactly. Remarkable structure both in the density of states and in the dynamical conductivity is found. Finally, we systematically derive the retraceable path approximation by Brinkman and Rice via a self-consistent 1/d expansion, which is correct up to order 1/

{\mathit{d}}^{4}

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.