Origin of strong dispersion in Hubbard insulators

Abstract

Using cluster perturbation theory, we explain the origin of the strongly dispersive feature found at high binding energy in the spectral function of the Hubbard model. By comparing the Hubbard and t−J−3s model spectra, we show that this dispersion does not originate from either coupling to spin fluctuations (∝ J) or the free hopping (∝ t). Instead, it should be attributed to a long-range, correlated hopping ∝ t 2 /U , which allows an effectively free motion of the hole within the same antiferromagnetic sublattice. This origin explains both the formation of the high energy anomaly in the single-particle spectrum and the sensitivity of the high binding energy dispersion to the next-nearest-neighbor hopping t ′ .PACS numbers: 71.10. Fd, 74.72.Cj, I. INTORDUCTIONHigh-temperature superconductivity in the cuprate oxides has attracted significant attention over the past thirty years. However, the precise origin of this phenomenon is not well understood due to the complex physics even in a minimal model used to describe the correlated nature of the electrons [1][2][3] : the 2D Hubbard model. It is often assumed that a first step in understanding the physics of this model is to study its spectral properties 4-17 in the simple undoped limit. The spectral function of the undoped 2D Hubbard model when the free electron bandwidth W is comparable to the Hubbard interaction U consists of two prominent features in the band structure, cf. Fig. 1. At low binding energies (LBE), a sharply defined quasiparticle-like excitation disperses downward from (π/2, π/2) reaching an energy of the order of spin exchange J = 4t 2 /U near the Γ-point (0,0). This quasiparticle, often labeled the spin polaron (SP) 18 , represents a hole heavily dressed by spin excitations from the antiferromagnetic (AF) ground state with its bandwidth no longer governed by the free electron hopping t but by the spin exchange J 9,18-23 . At higher binding energies (HBE), another feature becomes prominent approaching the Γ-point. The delineation of the LBE spin polaron from the HBE feature has been widely associated with the "high energy anomaly" or "waterfall" seen in a number of cuprate photoemission results 11,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] . While the spin polaron is well understood, the characterization remains poor for the feature at higher energies. One may naively expect that a broad, non-dispersive Hubbard band should appear at the Γ-point. However, as shown in Fig. 1, it is clear that there is a sharp dispersion. Previous studies have attributed this feature to scenarios such as spin-charge separation 16,17,34,35,[41][42][43][44][45] or a weak-coupling spin-density wave 9,10,46 . However, these interpretations remain controversial.The aim of this paper is to understand the nature of the HBE feature and what separates it from the SP. Using cluster perturbation theory we examine both the Hubbard, t−J and t−J−3s models to provide an in-depth examination of what controls the quasiparticle dispersion and int...

Revealing the Coulomb interaction strength in a cuprate superconductor

“…[26] attributed feature α purely to the UHB, which is an unoccupied state. However, the UHB is highly dispersive across the Brillouin zone [31,35,36], which is inconsistent with our observation on feature α. We emphasize that the modulation in intensity due to initial-state dispersions is key to understanding the origin of feature α.…”

Doping and temperature evolution of pseudogap and spin-spin correlations in the two-dimensional Hubbard model

“…Whereas CPT has been extensively used to study doping dependent electronic structure of models of strong electronic correlations at zero temperature 28,29,46,[51][52][53][54][55][56][57][58] and applied several times at finite temperatures 59,60 , to our knowledge there exists no detailed investigation of the temperature dependence of the pseudogap within CPT. Although CPT is not a self-consistent method (contrary to VCA or CDMFT) and thus cannot be used by itself to study ordered phases, since the pseudogap is a normal state phenomenon, CPT is fully applicable in our case.…”

Charge dynamics of the antiferromagnetically ordered Mott insulator

“…The bandwidth of the spin polaron is governed by the spin exchange, J, and this feature forms the low-energy part of the lower Hubbard band. For the high-energy part, hole motion is thought to originate from effective three-site hopping processes [38], which allow hole propagation on the same sublattice that does not distort the antiferromagnetic background and therefore is less affected by spin fluctuations. We postpone a more detailed discussion of the Hubbard bands to the next section.…”

“…For the intermediate-coupling regime, where no well-controlled theoretical solution exists, many numerical methods have been applied to the two-dimensional (2D) Hubbard model, including exact diagonalisation [20][21][22][23][24], quantum Monte Carlo [25][26][27][28][29][30][31][32], cluster perturbation theory [33][34][35][36][37][38], the variational cluster approximation [39][40][41][42][43] and cluster DMFT [44][45][46][47][48][49]. A detailed review, including further results from density-matrix renormalisation-group (DMRG) calculations, may be found in [50].…”