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arXiv:cond-mat/9609019 · Physical review. B, Condensed matter

Theory of the density fluctuation spectrum of strongly correlated electrons

Giniyat Khaliullin, Peter Horsch

Published Oct 1, 1996• 49 citations
arXivHTMLPDF

Abstract

The density response function $N(\mathrm{q}, \ensuremath{\omega})$ of the two-dimensional $t\ensuremath{-}J$ model is studied starting from a mixed-gauge formulation of the slave-boson approach. Our results for $N(\mathrm{q}, \ensuremath{\omega})$ are in remarkable agreement with exact diagonalization studies, and provide a natural explanation of the anomalous features in the density response in terms of the spin-polaron nature of the charge carriers. In particular, we have identified unexplained low-energy structures in the diagonalization data as arising from the coherent polaron motion of holes in a spin liquid.

DOI
10.1103/physrevb.54.r9600

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The density response function N(q,\ensuremathω)N(\mathrm{q}, \ensuremath{\omega})N(q,\ensuremathω) of the two-dimensional t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model is studied starting from a mixed-gauge formulation of the slave-boson approach. Our results for N(q,\ensuremathω)N(\mathrm{q}, \ensuremath{\omega})N(q,\ensuremathω) are in remarkable agreement with exact diagonalization studies, and provide a natural explanation of the anomalous features in the density response in terms of the spin-polaron nature of the charge carriers. In particular, we have identified unexplained low-energy structures in the diagonalization data as arising from the coherent polaron motion of holes in a spin liquid.
We investigate the dynamical spin and charge correlation functions, $S(\mathrm{Q}, \ensuremath{\omega})$ and $N(\mathrm{Q}, \ensuremath{\omega})$, for the two-dimensional (2D) $t\ensuremath{-}J$ model by using the exact diagonalization technique. Both quantities are compared with the 1D $t\ensuremath{-}J$ model. At high electron density (n>0.7n>0.7n>0.7), a remarkable feature emerges: $S(\mathrm{Q}, \ensuremath{\omega})$ shows a pronounced peak at low energy of order JJJ which is consistent with 2kF2{k}_{F}2kF​ low-energy excitations, whereas low-energy 2kF2{k}_{F}2kF​-backscattering processes are strongly suppressed in the charge-density response. $N(\mathrm{Q}, \ensuremath{\omega})$ consists of a dense and broad continuum, qualitatively different from the 1D charge response, implying strong interactions between charge and spin degrees of freedom.
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 ttt and JJJ. 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.
The density response of a doped Mott‐Hubbard insulator is discussed starting from the t‐J model in a slave boson 1/N representation. In leading order O(1) the density fluctuation spectra N(q, ω) are determined by an undamped collective mode at large momentum transfer, in striking disagreement with results obtained by exact diagonalization, which reveal a very broad dispersive peak, reminescent of strong spin‐charge coupling. The 1/N corrections introduce the polaron character of the bosonic holes moving in a uniform RVB background. The resulting N(q, ω) captures all features observed in diagonalization studies, fulfills the appropriate sum rules, and apart from the broadening of the collective mode shows a new low energy feature at the energy χJ + δt related to the polaron motion in the spinon background. It is further shown that the low energy structure, which is particularly pronounced in (π, 0) direction, describes the strong renormalization and anomalous damping of the highest bond‐stretching phonons in La2−xSrxCuO4.
We present an exact diagonalization study of the dynamical spin and density correlation functions in small clusters of the t-J model, focusing on the regime of intermediate and low electron densities, ${\mathrm{\ensuremath{\rho}}}_{\mathit{e}}$0.5. In two dimensions (2D) both correlation functions agree remarkably well with the convolution of the single-particle spectral function, i.e., the simplest estimate possible within a Fermi-liquid picture. Deviations from the convolution are shown to originate from symmetry-related selection rules, which are unaccounted for in the convolution estimate. For all fillngs under consideration, we show that the low-energy peaks originate from particle-hole excitations between the Fermi momenta, as expected for a Fermi liquid. We contrast this with the behavior in 1D, where spin and density correlation function show the differences characteristic of spin-charge separation and where neither correlation function is approximated well by the convolution.
The one-electron spectral function $\ensuremath{\rho}(\mathit{k},\ensuremath{\omega})$ for the large-N\mathcal{N}N $t\ensuremath{-}J$ model typically consists of two distinct peaks: a dispersive quasiparticle and a lower-energy incoherent structure. This is reminiscent of the spectral function of the weak coupling Hubbard model in which the electron is coupled to antiferromagnetic spin fluctuations. In both theories, the two-peaked pattern can be traced to the frequency dependence of the (normal) electron self-energy $\ensuremath{\Sigma}(\mathit{k},\ensuremath{\omega})$. What interaction causes this particular $\ensuremath{\omega}$ dependence of $\ensuremath{\Sigma}$? In the weak coupling case it is clearly the emission and absorption of an antiferromagnetic spin fluctuation by the electron. In the slave boson formulation of the large-N\mathcal{N}N $t\ensuremath{-}J$ model, there are six bosonic excitations: the slave bosons, the constraint field, and the real and imaginary parts of the hopping amplitudes in both the x and y directions. None of these are obviously related to a spin fluctuation propagator. These bosons have the unusual property of transmuting in flight---that is, they are not eigenstates. In order to try to make physical sense of the interaction that is primarily responsible for the frequency dependence of $\ensuremath{\Sigma}$ and the structure of $\ensuremath{\rho}(\mathit{k},\ensuremath{\omega})$, we investigate the transformation to a representation in which the boson propagator matrix is diagonal and extract the contributions of the slave bosons and the constraint field, which appear to be of particular importance.
The interplay between spin and charge degrees of freedom arising from doping a Mott insulating quantum spin liquid (QSL) has been a topic of research for several decades. Calculating properties of these fractionalized metallic states in single-band models are generally restricted to mean-field patron descriptions and small fluctuations around these states, which are insufficient for quantitative comparison of observables to measurements performed in strongly-correlated systems. In this work, we numerically study a class of correlated electronic wavefunctions which support fractionalized spin and charge excitations and which fully take into account gauge fluctuations through the enforcement of local Hilbert space constraints. By optimizing the energy of these wavefunctions against the hole-doped Fermi Hubbard Hamiltonian, we obtain a variational ansatz for describing the low-energy physics of this model. We compare measurements of hole-induced spin-spin correlation functions to measurements taken in low temperature cold-atom simulations of the Hubbard model and find quantitative agreement between the two. In particular, we demonstrate the emergence of magnetic polaron correlations in these metallic states.