Derivation of the t-J model for finite doping

Abstract

Mapping complex problems to simpler effective models is a key tool in theoretical physics. One important example in the realm of strongly correlated fermionic systems is the mapping of the Hubbard model to a t-J model which is appropriate for the treatment of doped Mott insulators. Charge fluctuations across the charge gap are eliminated. So far the derivation of the t-J model is only known at half-filling or in its immediate vicinity. Here we present the necessary conceptual advancement to treat finite doping. The results for the ensuing coupling constants are presented. Technically, the extended derivation relies on self-similar continuous unitary transformations (sCUT) and normal-ordering relative to a doped reference ensemble. The range of applicability of the derivation of t-J model is determined as function of the doping $\delta$ and the ratio bandwidth W over interaction U.

20 pages, 31 figures

References in corpus (7)

• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Screened Coulomb interaction in the maximally localized Wannier basis
• One- and Two-Triplon Spectra of a Cuprate Ladder
• Unifying variational methods for simulating quantum many-body systems
• Electron spectra close to a metal-to-insulator transition
• Systematic Mapping of the Hubbard Model to the Generalized t-J Model
• Coulomb parameters and photoemission for the molecular metal TTF-TCNQ

Cited by in corpus (6)

• Effective models for gapped phases of strongly correlated quantum lattice models
• Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices
• Dispersive Excitations in the One-Dimensional Ionic Hubbard Model
• Truncation errors in self-similar continuous unitary transformations
• Effective Models for the Anderson Impurity and the Kondo Model from Continuous Unitary Transformations
• Comparison of computer-algebra strong-coupling perturbation theory and dynamical mean-field theory for the Mott-Hubbard insulator in high dimensions