Photoemission spectra for the isotropic two-leg $t\ensuremath{-}J$ ladder are calculated at various hole-doping levels using exact diagonalization techniques. Low-energy sharp features caused by short-range antiferromagnetic correlations are observed at finite doping levels close to half-filling, above the naive Fermi momentum. These features should be observable in angle-resolved photoemission experiments. In addition, the formation of a
d-wave pairing condensate as the ratio
tJ is increased leads to dynamically generated spectral weight for momenta close to
kF where the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ order parameter is large.
Quantum Monte Carlo (QMC) and maximum-entropy techniques are used to study the spectral function $A(\mathbf{p},\ensuremath{\omega})$ of the one-band Hubbard model with strong coupling including a next-nearest-neighbor electronic hopping with amplitude ${t}^{\ensuremath{'}}/t=\ensuremath{-}0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for
Sr2CuO2Cl2. A narrow quasiparticle (qp) band is observed in the QMC analysis at the temperature of the simulation
T=t/3, both at and away from half-filling. Such a narrow band produces a large accumulation of weight in the density of states at the top of the valence band. As the electronic density
〈n〉 decreases further away from half-filling, the chemical potential travels through this energy window with a large number of states, and by $〈n〉\ensuremath{\sim}0.70$ it has crossed it entirely. The region near momentum $(0,\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ in the spectral function is more sensitive to doping than momenta along the diagonal from
(0,0) to $(\ensuremath{\pi},\ensuremath{\pi})$. The evolution with hole density of the quasiparticle dispersion contains some of the features observed in recent ARPES data in the underdoped regime. For sufficiently large hole densities the ``flat'' bands at $(\ensuremath{\pi},0)$ cross the Fermi energy, a prediction that could be tested with ARPES techniques applied to overdoped cuprates. The population of the qp band introduces a hidden density in the system which produces interesting consequences when the quasiparticles are assumed to interact through antiferromagnetic fluctuations and studied with the BCS gap-equation formalism. In particular, a region of extended
s-wave character is found to compete with the
d wave in the overdoped regime, i.e., when the chemical potential has almost entirely crossed the qp band as
〈n〉 is reduced. The present study also shows that previous ``real-space'' pairing theories for the cuprates, such as the antiferromagnetic Van Hove scenario, originally constructed based on information gathered at half-filling, do not change their predictions if hole dispersions resembling noninteracting electrons with renormalized parameters are used.
Literature addressing the existence of ``hole pockets'' in experiments for the high-
Tc cuprates and in theoretical analysis of electronic models of correlated electrons is reviewed. It is argued that the issue is not conclusively resolved, both in theory and experiments. The apparently large Fermi surface observed in numerical studies of the doped Hubbard and t-J models suggests the presence of 1-x carriers (with x the concentration of holes). However, this is in contradiction with results obtained in similar calculations for the Drude weight which scales with x at low doping. To address such a paradox, dressed operators are here used. Their spectral decomposition A(k,\ensuremath{\omega}) is analyzed specially using the t-J model on ladders, but considering also chains and two-dimensional (2D) clusters. The results are contrasted against those obtained with the standard bare operators. It is concluded that substantial changes in the spectral weight can occur by replacing the bare hole creation operator by its dressed version. Apparently large Fermi surfaces can turn into small ones by working with quasiparticle (qp) operators that represent accurately the state of one hole. Thus, large Fermi surfaces in angle-resolved photoemission (ARPES), obtained by the sudden removal of an electron, may not be in contradiction with a visualization of the normal state of lightly doped antiferromagnets as composed of a gas of spin polarons with energies approximately obtained from the rigid band doping of the half-filled dispersion. The coexistence of a large Fermi surface in ARPES with, e.g., a holelike Hall coefficient seems possible in systems with strong correlations. In this paper the expression ``hole pocket'' is used as representing a large accumulation of spectral weight centered at k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) generated by antiferromagnetic correlations in 2D clusters, or in analogous positions for ladders and chains. The subtle issue of whether such hole pockets represent a true small Fermi surface or just large incoherent weight cannot be addressed with finite resolution techniques such as angle-resolved photoemission and numerical studies of electronic models. They only provide information about the location of the dominant weight in A(k,\ensuremath{\omega}). The ideas discussed here are very general and they can be applied to a variety of problems where quasiparticles are strongly dressed by low energy excitations of the medium in which they are immersed.
The internal structure of doped holes in the Mott insulator may provide important insight into the physics of doped cuprates. Its observability via a single-particle probe by scanning tunneling spectroscopy (STS) and angle-resolved photoemission spectroscopy (ARPES) is explored in this paper. Specifically, we study the single-particle spectral function based on a two-hole variational ground-state wave function [J.-Y. Zhao et al., Phys. Rev. X 12, 011062 (2022)] in the $t\text{\ensuremath{-}}J$ model. The latter as a strongly correlated state possesses a dichotomy of
d-wave Cooper pairing and
s-wave ``twisted'' hole pairing. This pairing structure will give rise to two branches of local spectral function at finite energies. The low-lying one corresponds to a nodal-like quasiparticle excitation and the higher branch is associated with the pair breaking of ``twisted'' quasiparticles, with the threshold energy resembling a pseudogap, which is consistent with the recent STS observation. It can be further extended into energy spectra in momentum space measurable by ARPES, where the low-energy dispersion is also shown to agree well with the quantum Monte Carlo numerical result for a single hole. It implies that the dominant pairing force arises from the twisted holes showing up in the high-energy branch. The effect of the next-nearest-neighbor hopping integral ${t}^{\ensuremath{'}}$ is also examined, which shows an interesting distinction between ${t}^{\ensuremath{'}}/t>0$ and ${t}^{\ensuremath{'}}/t\ensuremath{\le}0$ with a dramatic shift of the low-lying excitation from the nodal region to the antinodal region, but with the high-energy branch remaining insensitive to ${t}^{\ensuremath{'}}$. Finally, a possible ``orthogonality catastrophe'' effect, namely, a ``dark matter'' component in the strongly correlated wave function that cannot be directly detected by the single-electron spectroscopy, is briefly discussed.
We investigate the effect of doping in the hole spectral function by exact diagonalization of a 16-site cluster with two holes. It is shown that for more than one hole the spectral function differs qualitatively from the one in the single-hole limit. In particular, we find no evidence for the formation of a Fermi surface having hole ``pockets'' localized around (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) in momentum space. On the contrary, a large low-energy peak appears in the spectral function of the hole propagator at k=(\ensuremath{\pi},0) or (0,\ensuremath{\pi}) which is then the best candidate for the existence of those pockets. A (\ensuremath{\pi}/2,\ensuremath{\pi}/2) quasihole state is obtained as a small energy excitation of the two-hole system. We discuss some consequences for photoemission and optical-conductivity experiments in high-
Tc materials at intermediate doping.
The two-dimensional $t\ensuremath{-}J$ model with and without ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ hopping-terms is studied by exact diagonalization on a $5\ifmmode\times\else\texttimes\fi{}4$ cluster, which realizes a hole stripe in y direction in a spin-Peierls phase. Next nearest hopping terms with a sign appropriate for hole-doped cuprates enhance the stripe formation. The dispersion of the quasiparticle peaks in the single-particle spectrum is in good agreement with bond operator theory for hole motion in the spin-Peierls phase, particularly so for realistic values of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}.$ The resulting spectral weight distribution and Fermi surface agree well with experimental angle-resolved photoemission spectra on
La1.28Nd0.6Sr0.12CuO4.