A numerical study of two-dimensional t-t'-J model at low hole density

The Hubbard model H = - t Zc~,cr, + U Xn~T n~, with N electrons and periodic boundary condition is studied on v-dimensional L~ x .-. x L~ lattices. It is shown that for any value of U there is no ground state with maximal spin (S = N/2) in the following cases: (i) 7/~ (v > 2) at low electron densities; with one hole if t > 0 and L~ is odd for some i; with two holes if t 0 and all the L~ are even. (ii) The bcc lattice at low densities; with two holes if t 0 and all the L~ are even; with 2 ..... 6 holes if L~ = Land t 0 and L is even. (iii) The triangular lattice at densities near 0 and 1 if t > 0; with two holes if t 0; with two holes if t < 0. Some results for the one dimensional model are also presented.The Hubbard model H = - t Zc~,cr, + U Xn~T n~, with N electrons and periodic boundary condition is studied on v-dimensional L~ x .-. x L~ lattices. It is shown that for any value of U there is no ground state with maximal spin (S = N/2) in the following cases: (i) 7/~ (v > 2) at low electron densities; with one hole if t > 0 and L~ is odd for some i; with two holes if t 0 and all the L~ are even. (ii) The bcc lattice at low densities; with two holes if t 0 and all the L~ are even; with 2 ..... 6 holes if L~ = Land t 0 and L is even. (iii) The triangular lattice at densities near 0 and 1 if t > 0; with two holes if t 0; with two holes if t < 0. Some results for the one dimensional model are also presented.

Jan 1, 19910 citations

Hole and pair structures in the t-J model

Steven R. White, Douglas J. Scalapino

Using numerical results from density matrix renormalization group (DMRG) calculations for the t-J model, on systems as large as 10\ifmmode\times\else\texttimes\fi{}7, we examine the structure of the one and two hole ground states in ladder systems and in two dimensional clusters. A simple theoretical framework is used to explain why holes bind in pairs in two-dimensional antiferromagnets. For the case J/t=0.5, which we have studied, the hole pairs reside predominantly on a 2\ifmmode\times\else\texttimes\fi{}2 core plaquette with the probability that the holes are on diagonal sites greater than nearest-neighbor sites. There is a strong singlet bond connecting the spins on the two remaining sites of the plaquette. We find that a general characteristic of dynamic holes in an antiferromagnet is the presence of frustrating antiferromagnetic bonds connecting next-nearest-neighbor sites across the holes. Pairs of holes bind in order to share the frustrating bonds. At low doping, in addition to hole pairs, there are two additional low-energy structures which spontaneously form on certain finite systems. The first is an undoped L\ifmmode\times\else\texttimes\fi{}2 spin-liquid region, or ladder. The second is a hole moving along a one dimensional chain of sites. At higher doping we expect that hole pairing is always favored.Using numerical results from density matrix renormalization group (DMRG) calculations for the t-J model, on systems as large as 10\ifmmode\times\else\texttimes\fi{}7, we examine the structure of the one and two hole ground states in ladder systems and in two dimensional clusters. A simple theoretical framework is used to explain why holes bind in pairs in two-dimensional antiferromagnets. For the case J/t=0.5, which we have studied, the hole pairs reside predominantly on a 2\ifmmode\times\else\texttimes\fi{}2 core plaquette with the probability that the holes are on diagonal sites greater than nearest-neighbor sites. There is a strong singlet bond connecting the spins on the two remaining sites of the plaquette. We find that a general characteristic of dynamic holes in an antiferromagnet is the presence of frustrating antiferromagnetic bonds connecting next-nearest-neighbor sites across the holes. Pairs of holes bind in order to share the frustrating bonds. At low doping, in addition to hole pairs, there are two additional low-energy structures which spontaneously form on certain finite systems. The first is an undoped L\ifmmode\times\else\texttimes\fi{}2 spin-liquid region, or ladder. The second is a hole moving along a one dimensional chain of sites. At higher doping we expect that hole pairing is always favored.

arXiv:cond-mat/9605143Physical review. B, Condensed matterMar 1, 1997165 citations

Dynamics of a single hole in the $t-J$ modelDynamics of a single hole in the $t-J$ model

Fabian Grusdt, Márton Kanász-Nagy, Annabelle Bohrdt +1 more

Bulletin of the American Physical SocietyMar 13, 20170 citations

Hole motion in one-dimensional t-J-J’ model

Ippei Doi, Kazuhiro Sano, Ken'ichi Takano

Physica B Condensed MatterAug 1, 19906 citations

Electron-electron interaction in a two-dimensional electron gas: Bound states at low densities

I. Nagy, Martti J. Puska, Nerea Zabala

If the bare interaction between two electrons is dressed in the two-dimensional electron gas by the response of the many-body environment, pairing may occur. Here, we study numerically the existence and character of bound states in the case where the dressing in the pair-interaction energy is described by the Overhauser geminal model [A. W. Overhauser, Can. J. Phys. 75, 683 (1995)]. The starting point of the model is the exchange correlation hole around a single electron. We constrain the hole by arguments based on the results for the exchange-correlation energy and the contact density of the pair-correlation function. We find a bound state with the energy minimized at a certain electron gas density. On the basis of the behavior of the binding energy we discuss recent experimental findings for the electron density dependence of the critical temperature in cuprate, Chevrel-phase, and Li-intercalated ${\mathrm{Li}}_{x}\mathrm{Zr}\mathrm{N}\mathrm{Cl}$ superconductors.If the bare interaction between two electrons is dressed in the two-dimensional electron gas by the response of the many-body environment, pairing may occur. Here, we study numerically the existence and character of bound states in the case where the dressing in the pair-interaction energy is described by the Overhauser geminal model [A. W. Overhauser, Can. J. Phys. 75, 683 (1995)]. The starting point of the model is the exchange correlation hole around a single electron. We constrain the hole by arguments based on the results for the exchange-correlation energy and the contact density of the pair-correlation function. We find a bound state with the energy minimized at a certain electron gas density. On the basis of the behavior of the binding energy we discuss recent experimental findings for the electron density dependence of the critical temperature in cuprate, Chevrel-phase, and Li-intercalated ${\mathrm{Li}}_{x}\mathrm{Zr}\mathrm{N}\mathrm{Cl}$ superconductors.

Physical Review BJun 29, 20072 citations

Dynamics of a single hole in the

t-J

model

{\mathrm{Li}}_{x}\mathrm{Zr}\mathrm{N}\mathrm{Cl}

superconductors.