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

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Cited by in corpus (16)

• Time Evolution of Many-Body Localized Systems with the Flow Equation Approach
• Enhanced Perturbative Continuous Unitary Transformations
• Self-consistent spin-wave theory for a frustrated Heisenberg model with biquadratic exchange in the columnar phase and its application to iron pnictides
• Effective models for gapped phases of strongly correlated quantum lattice models
• Effects of ring exchange interaction on the Neel phase of two-dimensional, spatially anisotropic, frustrated Heisenberg quantum antiferromagnet
• Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices
• Polaronic mechanism of Nagaoka ferromagnetism in Hubbard models
• Dispersive Excitations in the One-Dimensional Ionic Hubbard Model
• Orientational bond and Néel order in the two-dimensional ionic Hubbard model
• Double-Exchange Enhanced Magnetic Blue-Shift of Mott Gaps
• Truncation errors in self-similar continuous unitary transformations
• Effective Models for the Anderson Impurity and the Kondo Model from Continuous Unitary Transformations
• Hole Dispersions for Antiferromagnetic Spin-1/2 Two-Leg Ladders by Self-Similar Continuous Unitary Transformations
• Evaluation of High Order Terms for the Hubbard Model in the Strong-coupling Limit
• Charge dynamics in magnetically disordered Mott insulators
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