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arXiv:cond-mat/9505145 · Physical review. B, Condensed matter

Hole dynamics in generalized spin backgrounds in infinite dimensions

K. Hallberg, E. Müller‐Hartmann, C. A. Balseiro

Published Aug 1, 1995• 2 citations
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Abstract

We calculate the dynamical behavior of a hole in various spin backgrounds in infinite dimensions, where it can be determined exactly. We consider hypercubic lattices with two different types of spin backgrounds. On one hand we study an ensemble of spin configurations with an arbitrary spin probability on each sublattice. This model corresponds to a thermal average over all spin configurations in the presence of staggered or uniform magnetic fields. On the other hand we consider a definite spin state characterized by the angle between the spins on different sublattices, i.e., a classical spin system in an external magnetic field. When spin fluctuations are considered, this model describes the physics of unpaired particles in strong-coupling superconductors.

DOI
10.1103/physrevb.52.4396

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We calculate the dynamical behavior of a hole in various spin backgrounds in infinite dimensions, where it can be determined exactly. We consider hypercubic lattices with two different types of spin backgrounds. On one hand we study an ensemble of spin configurations with an arbitrary spin probability on each sublattice. This model corresponds to a thermal average over all spin configurations in the presence of staggered or uniform magnetic fields. On the other hand we consider a definite spin state characterized by the angle between the spins on different sublattices, i.e., a classical spin system in an external magnetic field. When spin fluctuations are considered, this model describes the physics of unpaired particles in strong-coupling superconductors.
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/d2{\mathit{d}}^{2}d2 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/d4{\mathit{d}}^{4}d4.
The dynamical properties of hole motion in an antiferromagnetic background are determined in one-dimensional models in zero magnetic field, where spin isotropy holds, as well as in an external magnetic field. The latter case is also relevant, via particle-hole transformation, to the problem of hole propagation in one-dimensional ``superconductors.'' The singularities in the spectral function are investigated by means of bosonization techniques and perturbation theories. Results are then compared with Bethe ansatz solutions and Lanczos diagonalizations. The formalism also leads to interesting connections to the single impurity problem in Luttinger liquids. A rich structure is found in the spectral function whenever spin isotropy is broken, suggesting the presence of exotic momentum dependence in photoemission spectra of (quasi) one dimensional materials.
The ground state of the two-dimensional Hubbard model on a square lattice is studied in the large-U limit in a half-filled band with a dynamical hole. For a 4\ifmmode\times\else\texttimes\fi{}4 lattice with hopping t=1 and coupling JJc{J}_{c}Jc​\ensuremath{\approxeq}0.075, the ground state has zero momentum (k) and spin 15/2 (ferromagnetic background). For J\ensuremath{\ge}Jc{J}_{c}Jc​ 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.
We discuss recent applications of exact numerical continued fraction expansion (CFE) techniques to calculate dynamical correlation functions of various strong-coupling models related to the high-temperature cuprate superconductors. For the two-dimensional square-lattice spin-1/2 Heisenberg antiferromagnet, we present exact results for the zero-temperature dynamical structure factor on finite-sized lattices and compare them to approximate results from a Schwinger boson mean-field theory, recently proposed by Arovas and Auerbach. We find that the mean-field theory represents a very good approximation to the exact spin excitation spectra and to the static spin correlations. We then investigation the dynamical spin-spin structure factor and the single-particle spectral function for finite model clusters with dopant induced hole-type charge carriers, in the strong-coupling limit of both the single-band Hubbard model (t-J-model) and the three-band Hubbard model (Kondo-Heisenberg model). Our results are consistent with the physical picture recently proposed by Zhang and Rice which implies an approximate mapping of the low-energy states in the three-band model onto an effective single-band theory. 33 refs., 4 figs.
We investigate the interplay between the formation of a lattice and magnetic polaron in the case of a single hole in the antiferromagnetic background. We present an exact analytical solution of the Holstein $t\ensuremath{-}J$ model in infinite dimensions. The ground-state energy, electron-lattice correlation function, spin bag dimension as well as spectral properties are calculated. The magnetic and hole-lattice correlations sustain each other, i.e., the presence of antiferromagnetic correlations favors the formation of the lattice polaron at lower values of the electron-phonon coupling while the polaronic effect contributes to reduce the number of spin defects in the antiferromagnetic background. The crossover towards a spin-lattice small polaron region of the phase diagram becomes a discontinuous transition in the adiabatic limit.