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.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.

arXiv:cond-mat/9304044Physical review. B, Condensed matterMay 1, 199445 citations

Holes in a Quantum Antiferromagnet: New Approach and Exact Results

R. Shankar

Physical Review LettersAug 28, 19893 citations

Cumulant-expansion study of holes in quantum antiferromagnets

P. Prelovek, Igor Sega, J. Bona

The states of a single hole and of two holes in the planar quantum antiferromagnet are studied within the t-J model by performing the cumulant expansion in t/J and in the exchange anisotropy \ensuremath{\gamma}. Ground-state energies are calculated up to the n=12 order in t/J and to the m=6 order in \ensuremath{\gamma}. It is shown that results, which can be extended to smaller J/t, represent a very helpful supplement to exact diagonalization methods. In particular they yield finite-size corrections to previous results on the dispersion of single-hole states and to the binding energy of two holes, giving also more insight into the origin of binding.The states of a single hole and of two holes in the planar quantum antiferromagnet are studied within the t-J model by performing the cumulant expansion in t/J and in the exchange anisotropy \ensuremath{\gamma}. Ground-state energies are calculated up to the n=12 order in t/J and to the m=6 order in \ensuremath{\gamma}. It is shown that results, which can be extended to smaller J/t, represent a very helpful supplement to exact diagonalization methods. In particular they yield finite-size corrections to previous results on the dispersion of single-hole states and to the binding energy of two holes, giving also more insight into the origin of binding.

Physical review. B, Condensed matterDec 1, 199022 citations

Hole excitations in quantum antiferromagnets

Efstratios Manousakis

Nuclear Physics B - Proceedings SupplementsMay 1, 19912 citations

Dynamics of a hole in a quantum antiferromagnet

Annabelle Bohrdt, Fabian Grusdt, Michael Knap +7 more

Bulletin of the American Physical SocietyMar 4, 20200 citations

Exact-diagonalization study of the effective model for holes in the planar antiferromagnet

J. Bonča, Peter Prelovšek, Igor Sega

The effective single-band Hamiltonian for holes in the two-dimensional quantum antiferromagnet, relevant for the ${\mathrm{CuO}}_{2}$ layers in copper-oxide superconductors, is studied by the exact diagonalization of a finite-size system with 16 cells. Single- and two-hole ground-state properties are calculated. Pair-binding-energy and hole-density correlation functions indicate that two holes bind for moderate exchange interactions, even in the case of the extreme anisotropic-Ising limit.The effective single-band Hamiltonian for holes in the two-dimensional quantum antiferromagnet, relevant for the ${\mathrm{CuO}}_{2}$ layers in copper-oxide superconductors, is studied by the exact diagonalization of a finite-size system with 16 cells. Single- and two-hole ground-state properties are calculated. Pair-binding-energy and hole-density correlation functions indicate that two holes bind for moderate exchange interactions, even in the case of the extreme anisotropic-Ising limit.

Physical review. B, Condensed matterApr 1, 1989197 citations

{\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.

The effective single-band Hamiltonian for holes in the two-dimensional quantum antiferromagnet, relevant for the

{\mathrm{CuO}}_{2}

layers in copper-oxide superconductors, is studied by the exact diagonalization of a finite-size system with 16 cells. Single- and two-hole ground-state properties are calculated. Pair-binding-energy and hole-density correlation functions indicate that two holes bind for moderate exchange interactions, even in the case of the extreme anisotropic-Ising limit.