We investigate the dynamical charge-charge correlation function and the optical conductivity in weakly doped antiferromagnets using Mori-Zwanzig projection technique. The system is described by the two-dimensional t - J model. The arising matrix elements are evaluated within a cumulant formalism which was recently applied to investigate magnetic properties of weakly doped antiferromagnets. Within the present approach the ground state consists of non-interacting hole quasiparticles. Our spectra agree well with numerical results calculated via exact diagonalization techniques. The method we employ enables us to explain the features present in the correlation functions. We conclude that the charge dynamics at weak doping is governed by transitions between excited states of spin-bag quasiparticles.
We investigate the dynamical charge-charge correlation function and the optical conductivity in weakly doped antiferromagnets using Mori-Zwanzig projection technique. The system is described by the two-dimensional t - J model. The arising matrix elements are evaluated within a cumulant formalism which was recently applied to investigate magnetic properties of weakly doped antiferromagnets. Within the present approach the ground state consists of non-interacting hole quasiparticles. Our spectra agree well with numerical results calculated via exact diagonalization techniques. The method we employ enables us to explain the features present in the correlation functions. We conclude that the charge dynamics at weak doping is governed by transitions between excited states of spin-bag quasiparticles.
We present an exact-diagonalization study of the frequency- and wave-vector-dependent conductivity $\ensuremath{\sigma}(\mathrm{q}, \ensuremath{\omega})$ in small clusters in the two-dimensional $t\ensuremath{-}J$ model. Unlike the related dynamical density correlation function, $\ensuremath{\sigma}(\mathrm{q}=0, \ensuremath{\omega})$ in the underdoped regime has the exchange constant J as its characteristic energy scale and is dominated by a resonancelike excitation with frequency $\ensuremath{\sim}1.7J$. We interpret this as transition to a p-like excited state of a spin-bag-type quasiparticle (or, alternatively, a tightly bound spinon-holon pair) and show that a simple calculation based on the string picture explains the numerical results semiquantitatively. For doping levels >25 remains the only energy scale of $\ensuremath{\sigma}(\mathrm{q}=0, \ensuremath{\omega})$.
We present a nonperturbative method for deriving a quasiparticle description of the low-energy excitations in the t-J model for strongly correlated electrons. Using the exact diagonalization technique we evaluated exactly the spectral functions of composite operators, which describe an electron or hole dressed by antiferromagnetic spin fluctuations as expected in the string or spin bag picture. For hole doping up to 1/8, use of the composite operators leads to a drastic simplification of the single-particle spectral function: at half-filling it takes free-particle form, for the doped case it resembles a system of weakly interacting fermions corresponding to the doped holes. We conclude that for all doping levels studied, the elementary electronic excitations next to the Fermi level are adequately described by the antiferromagnetic spin-fluctuation picture.
Recent results for the finite-temperature static and dynamical properties of the planar t−J model, obtained by a novel numerical method for small correlated systems, are reviewed. Of particular interest are T>0 charge and spin response functions: optical conductivity σ(ω) and spin susceptibility χ(q,ω), which show very universal features at intermediate doping. In spin dynamics the universality is best seen in the local spin correlation function, which appears to be T-independent and only weakly doping dependent. Results apply directly to the inelastic neutron scattering and to the NMR relaxation experiments in cuprates. Analysing σ(ω) we find that the current correlation function C(ω) is nearly T- and moreover ω-independent in the regime $T
We present an exact diagonalization study of the dynamical spin and density correlation functions in small clusters of 2D $t\ensuremath{-}J$ model for hole dopings $\ensuremath{\le}25$%. Both correlation functions show a remarkably regular, but very different, scaling with both hole density ${\ensuremath{\rho}}_{h}$ and parameters t and J. The density correlation function is most consistent with that of condensed bosons in a band of width $\ensuremath{\sim}t$, the spin correlation function with that of fermions in a band of width $\ensuremath{\sim}J$. We show that the familiar spin bag scenario explains these results in a natural way.
We introduce a slave-fermion formulation in which to study the charge dynamics of the half-filled Hubbard model on the square lattice. In this description, the charge degrees of freedom are represented by fermionic holons and doublons and the Mott-insulating characteristics of the ground state are the consequence of holon–doublon bound-state formation. The bosonic spin degrees of freedom are described by the antiferromagnetic Heisenberg model, yielding long-ranged (Néel) magnetic order at zero temperature. Within this framework and in the self-consistent Born approximation, we perform systematic calculations of the average double occupancy, the electronic density of states, the spectral function and the optical conductivity. Qualitatively, our method reproduces the lower and upper Hubbard bands, the spectral-weight transfer into a coherent quasiparticle band at their lower edges and the renormalisation of the Mott gap, which is associated with holon–doublon binding, due to the interactions of both quasiparticle species with the magnons. The zeros of the Green function at the chemical potential give the Luttinger volume, the poles of the self-energy reflect the underlying quasiparticle dispersion with a spin-renormalised hopping parameter and the optical gap is directly related to the Mott gap. Quantitatively, the square-lattice Hubbard model is one of the best-characterised problems in correlated condensed matter and many numerical calculations, all with different strengths and weaknesses, exist with which to benchmark our approach. From the semi-quantitative accuracy of our results for all but the weakest interaction strengths, we conclude that a self-consistent treatment of the spin-fluctuation effects on the charge degrees of freedom captures all the essential physics of the antiferromagnetic Mott–Hubbard insulator. We remark in addition that an analytical approximation with these properties serves a vital function in developing a full understanding of the fundamental physics of the Mott state, both in the antiferromagnetic insulator and at finite temperatures and dopings.
To discuss the interplay of electronic and lattice degrees of freedom in systems with strong Coulomb correlations we have performed an extensive numerical study of the two-dimensional Holstein $t\ensuremath{-}J$ model. The model describes the interaction of holes, doped in a quantum antiferromagnet, with a dispersionsless optical phonon mode. We apply finite-lattice Lanczos diagonalization, combined with a well-controlled phonon Hilbert space truncation, to the Hamiltonian. The focus is on the dynamical properties. In particular we have evaluated the single-particle spectral function and the optical conductivity for characteristic hole-phonon couplings, spin exchange interactions, and phonon frequencies. The results are used to analyze the formation of lattice hole polarons in great detail. Links with experiments on layered perovskites are made. In addition, we compare the Chebyshev recursion and maximum entropy algorithms, used for calculating spectral functions, with standard Lanczos methods.