We develop here a general formalism for multiorbital Mott systems that can be used to understand dynamical and static spectral weight transfer. We find that the spectral weight transferred from the high-energy scales is greatly increased as a result of the multiorbital structure. As a consequence certainly dynamically generated symmetries are obtained at lower values of doping than in the single-band Hubbard model. For example, in the atomic limit for filling less than one electron per site, the particle-hole symmetric condition in the lower band shifts from the one-band result of
x=1/3 to
x=1/(2no+1), where
no is the number of orbitals with an unpaired spin. Transport properties computed from effective low-energy theories that forbid double occupancy of bare electrons, such as the multiorbital
t-
J generalization, should all be be sensitive to this particle-hole symmetric condition. Away from the atomic limit, the dynamical contributions increase the transferred spectral weight. Consequently, any phenomena that are sensitive to an emergent particle-hole symmetry should be obtained at
x<[1/(2no+1)].
We show that the physics of the SU(
N) Hubbard model can be realistically simulated with the recently developed orbital Hatsugai-Kohmoto model. In this approach, the momentum mixing absent from the band Hatsugai-Kohmoto model is included by grouping
n-Hubbard atoms into a cluster. We take advantage of the rapid convergence of this scheme (
1/n2) and show that for
n≈O(10), quantitative agreement with the determinantal quantum Monte Carlo method arises for the double occupancy as well as qualitative agreement for the filling and compressibility across the Mott transition. Additional features of this work are that we can obtain low-temperature physics, which could be qualitatively different from its high-temperature counterpart, and dynamical quantities without resorting to analytical continuation, thereby establishing the orbital Hatsugai-Kohmoto model as a useful alternative perspective for studying strong correlations in SU(
N) systems.
In this paper we study the spectral-weight transfer from the high- to the low-energy scale by means of exact diagonalization of finite clusters for the Mott-Hubbard and charge-transfer model. We find that the spectral-weight transfer is very sensitive to the hybridization strength as well as to the amount of doping. This implies that the effective number of low-energy degrees of freedom is a function of the hybridization and therefore of the volume and temperature. In this sense it is not possible to define a Hamiltonian which describes the low-energy-scale physics unless one accepts an effective nonparticle conservation.
We study entanglement in the Hatsugai-Kohmoto model, which exhibits a continuous interaction-driven Mott transition. By virtue of the all-to-all nature of its center-of-mass-conserving interactions, the model lacks dynamical spectral weight transfer, which is the key to the intractability of the Hubbard model for
d>1. In order to maintain a nontrivial Mott-like electron propagator, SU(2) symmetry is preserved in the Hamiltonian, leading to a ground state that is mixed on both sides of the phase transition. Because of this mixture, even the metal in this model is unentangled between any pair of sites, unlike free fermions whose ground state carries a filling-dependent site-site entanglement. We focus on the scaling behavior of the one- and two-site entropies
s1 and
s2, as well as the entropy density
s, of the ground state near the Mott transition. At low temperatures in the two-dimensional Hubbard model, Walsh et al. [Phys. Rev. B 99, 075122 (2019)] observed numerically that
s1 and
s increase continuously into the metal, across a first-order Mott transition. In the Hatsugai-Kohmoto model,
s1 acquires the constant value ln 4 even at the Mott transition. On the other hand,
s2 and
s each act as a sharp signal of the Mott transition, in any dimension, by decreasing at the transition into the metal. Specifically, we find that in one dimension,
s2 and
s exhibit kinks at the transition while in two dimensions, only
s exhibits a kink.
Using strong-coupling perturbation theory for the Hubbard model, explicit expressions are obtained for the integrated weights, energy positions, and widths of the upper and lower Hubbard bands separately, both for the optical and photoemission spectrum. In one dimension all expressions can be explicitly evaluated using the large-U Bethe-ansatz wave function. The k\ensuremath{\rightarrow}-dependent moments for the one-particle spectrum are compared with the closely related two-pole ansatz. The strong momentum dependence of the spectra demonstrates the importance of the k\ensuremath{\rightarrow}-dependent correlation functions in the spectral moments, which are often neglected. In order to estimate corrections due to the neglect of higher-order terms (in t/U), all results are compared with numerical-diagonalization data for intermediate-U values. The sum-rule results show a rapid spectral-weight transfer from the high- to the low-energy regime upon doping, similar to what is observed experimentally in one-particle and optical spectra of Cu (high-
Tc) and Ni compounds. Such fast weight redistributions as a function of the carrier density are a natural consequence of the strong correlations in these materials. The redistribution of intensity in the optical conductivity is connected with the dilution of the spin system by the added holes. For the one-particle spectrum the decrease of weight in the upper Hubbard band away from half filling can be understood by state counting at U=\ensuremath{\infty}, and the effect is strongly enhanced for small doping by both the first- and second-order terms in t/U. Altogether, the one-particle and optical spectra show the importance of the three-site hopping term. Therefore the t-J model does not represent well the spectral properties of the Hubbard model at large U. The local spin order is essential and determines both the k\ensuremath{\rightarrow} dependence of the one-particle spectrum and the intensities in the optical spectrum.