Motivated by the recent resonant inelastic x-ray scattering (RIXS) experiment for the electron-doped cuprates ${\mathrm{Nd}}_{2\ensuremath{-}x}{\mathrm{Ce}}_{x}{\mathrm{CuO}}_{4}$ with $x\ensuremath{\approx}0.15$, we compute the density-density correlation function in the $t\ensuremath{-}J$ model on a square lattice by including interlayer hopping and the long-range Coulomb interaction. We find that collective charge excitations are realized not inside the particle-hole continuum, but above the continuum as plasmons. The plasmon mode has a rather flat dispersion near the in-plane momentum ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$ with a typical excitation energy of the order of the intralayer hopping
t when the out-of-plane momentum
qz is zero. However, when
qz becomes finite, the plasmon dispersion changes drastically near ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$, leading to a strong dispersive feature with an excitation gap scaled by the interlayer hopping
tz. We discuss the mode recently observed by RIXS near ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$ in terms of the plasmon mode with a finite
qz.
We study the impact of next-nearest-neighbor (NNN) hopping on the low-energy collective excitations of strongly correlated doped antiferromagnetic cuprate spin chains. Specifically, we use exact diagonalization and the density matrix renormalization group method to study the single-particle spectral function, the dynamical spin and charge structure factors, and the Cu
L-edge resonant inelastic x-ray scattering (RIXS) intensity of the doped $t\text{\ensuremath{-}}t\ensuremath{'}\text{\ensuremath{-}}J$ model for a set of $t\ensuremath{'}$ values. We find evidence that the spin and charge degrees of freedom of the doped holes are not strictly separated anymore as $|t\ensuremath{'}|$ increases and identify the consequences of this in the dynamical response functions. The inclusion of NNN hopping couples the spinon and holon excitations, resulting in the formation of a spin polaron, where a ferromagnetic spin-polarization cloud dresses the doped carrier. The spin polaron manifests itself as additional spectral weight in the dynamical correlation functions, which appear simultaneously in the spin- and charge-sensitive channels. We also demonstrate that RIXS can provide a unique view of the spin polaron, due to its sensitivity to both the spin and charge degrees of freedom.
Hubbard excitons are bound states of doublons and holes that can be experimentally probed both in real materials, such as cuprates, and in cold atom quantum simulators. Here we compare properties of a Hubbard exciton to those of a pair of distinguishable dopants in the
t−J model and show how insights into pair properties can be obtained through excitonic spectra. In particular, we perform large-scale numerical simulations of spectral functions and optical conductivities and obtain remarkable agreement between Hubbard excitons and pairs of distinguishable dopants. The latter can be decomposed into symmetric (bosonic) and anti-symmetric (fermionic) sectors of indistinguishable dopants, thus enabling a detailed understanding of different features observed in the excitonic spectra through comparison with a semi-analytical geometric string theory approach. We further compare theoretically computed exciton spectra in a single band Fermi-Hubbard model to resonant inelastic X-ray scattering (RIXS) studies of the parent insulating cuprate materials. We find remarkable agreement between the two spectra in both energy and momentum dependence. Our analysis suggests that multiple long-lived ro-vibrational exciton resonances have been observed in RIXS spectra. Experimentally, these features are known to persist up to optimal doping. The comparison we provide between semi-analytical theory, large-scale numerics, and experimental data thus provides an explanation of the RIXS measurements and provides new insight into the nature of pairing in cuprates.
We provide a unified interpretation of both paramagnon and plasmon modes in high-
Tc copper-oxides, and verify it quantitatively against available resonant inelastic
x-ray scattering (RIXS) data across the hole-doped phase diagram. The three-dimensional extended Hubbard model, with included long-range Coulomb interactions and doping-independent microscopic parameters for both classes of quantum fluctuations, is used. Collective modes are studied using
VWF+1/Nf approach which extends variational wave function (VWF) scheme by means of an expansion in inverse number of fermionic flavors
(1/Nf). We show that intense paramagnons persist along the antinodal line from the underdoped to the overdoped regime and undergo rapid overdamping in the nodal direction. Plasmons exhibit a three-dimensional character, with minimal energy corresponding to antiphase oscillations on neighboring
CuO2 planes. The theoretical spin- and charge excitation energies reproduce semiquantitatively RIXS data for ${(\mathrm{Bi},\mathrm{Pb})}_{2}{(\mathrm{Sr},\mathrm{La})}_{2}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$. The present
VWF+1/Nf analysis of dynamics and former VWF results for static quantities combine into a consistent description of the principal properties of hole-doped high-
Tc cuprates as strongly correlated systems.
We study the dynamical, momentum-dependent two- and four-spin response functions in doped and undoped one-dimensional cuprates, as probed by resonant inelastic x-ray scattering, using an exact numerical diagonalization procedure. In the undoped
t--
J system, the four-spin response vanishes at $\ensuremath{\pi}$, whereas the two-spin correlator is peaked around $\ensuremath{\pi}/2$, with generally larger spectral weight. Upon doping, spectra tend to soften and broaden, with a transfer of spectral weight toward higher energy. However, the total spectral weight and average peak position of either response are only weakly affected by doping up to a concentration of 1/8. Only the two-spin response at $\ensuremath{\pi}$ changes strongly, with a large reduction of spectral weight and enhancement of excitation energy. At other momenta, the higher energy, generic features of the magnetic response are robust against doping. It signals the presence of strong short-range antiferromagnetic correlations, even after doping mobile holes into the system. We expect this to hold also in higher dimensions.
Motivated by the recent resonant x-ray scattering (RXS) and resonant inelastic x-ray scattering (RIXS) experiments for electron-doped cuprates, we study the charge excitation spectrum in a layered $t\text{\ensuremath{-}}J$ model with the long-range Coulomb interaction. We show that the spectrum is not dominated by a specific type of charge excitations, but by different kinds of charge fluctuations, and is characterized by a dual structure in the energy space. Low-energy charge excitations correspond to various types of bond-charge fluctuations driven by the exchange term (
J term), whereas high-energy charge excitations are due to usual on-site charge fluctuations and correspond to plasmon excitations above the particle-hole continuum. The interlayer coupling, which is frequently neglected in many theoretical studies, is particularly important to the high-energy charge excitations.