Physical review. B, Condensed matter

Coupled-cluster method applied to the motion of a single hole in a Hubbard antiferromagnet

F. Petit, M. Röger

Published Feb 1, 1994• 19 citations

Abstract

The coupled-cluster method has recently proved to be efficient in calculating the ground state of strongly interacting spins or fermions on lattices. We apply it to the ground state of one hole in the half-filled Hubbard model on a two-dimensional square lattice. In a wide range for the interaction 10\ensuremath{\lesssim}U/t\ensuremath{\lesssim}80, the ground-state energy of a hole is fitted by a simple function \ensuremath{\epsilon}/t\ensuremath{\approxeq}-3.40+8.9(t/U${)}^{0.70}$, in good agreement with the results obtained through exact diagonalizations on small clusters. The effective mass of a hole ${\mathit{m}}^{\mathrm{*}}$=8t/W (W represents the bandwidth) is proportional to U/T (${\mathit{m}}^{\mathrm{*}}$\ensuremath{\approxeq}0.845U/t) for 5\ensuremath{\lesssim}U/t\ensuremath{\lesssim}20 and saturates to a constant value ${\mathit{m}}^{\mathrm{*}}$\ensuremath{\approxeq}84 for large U/t.

DOI: 10.1103/physrevb.49.3453

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Physical review. B, Condensed matter

Coupled-cluster method applied to the motion of a single hole in a Hubbard antiferromagnet

F. Petit, M. Röger

Published Feb 1, 1994• 19 citations

Publisher

Abstract

{)}^{0.70}

, in good agreement with the results obtained through exact diagonalizations on small clusters. The effective mass of a hole

{\mathit{m}}^{\mathrm{*}}

=8t/W (W represents the bandwidth) is proportional to U/T (

{\mathit{m}}^{\mathrm{*}}

\ensuremath{\approxeq}0.845U/t) for 5\ensuremath{\lesssim}U/t\ensuremath{\lesssim}20 and saturates to a constant value

{\mathit{m}}^{\mathrm{*}}

\ensuremath{\approxeq}84 for large U/t.

DOI: 10.1103/physrevb.49.3453

Related papers

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{)}^{0.70}

, in good agreement with the results obtained through exact diagonalizations on small clusters. The effective mass of a hole

{\mathit{m}}^{\mathrm{*}}

=8t/W (W represents the bandwidth) is proportional to U/T (

{\mathit{m}}^{\mathrm{*}}

\ensuremath{\approxeq}0.845U/t) for 5\ensuremath{\lesssim}U/t\ensuremath{\lesssim}20 and saturates to a constant value

{\mathit{m}}^{\mathrm{*}}

\ensuremath{\approxeq}84 for large U/t.

K

-space excitation spectrum for a single hole. Within our finite-size system, it is found that for very small coupling ratio

\frac{t}{U}

, each hole creates a local ferromagnetic environment at least of the size of our system, whereas for increasing

\frac{t}{U}

, the holes tend to form clusters, induced by antiferromagnetic spin correlations. A range of

\frac{t}{U}

exists for which pairing of the holes may be possible.

{J}_{c}

\ensuremath{\approxeq}0.075, the ground state has zero momentum (k) and spin 15/2 (ferromagnetic background). For J\ensuremath{\ge}

{J}_{c}

the ground state is degenerate with nonzero k and spin 1/2, in agreement with recent variational calculations. The nonzero k of the ground state comes from a nontrivial phase in the overlap of the spin states before and after a hole move. For small lattices we show that the effective Hamiltonian of the hole is that of a particle moving in a magnetic field. We also find that many of the features of the weak-coupling region carry over continuously to the strong-coupling region.

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.