The Hubbard model beyond the two-pole approximation: a Composite Operator Method study

Abstract

Within the framework of the Composite Operator Method, a three-pole solution for the two-dimensional Hubbard model is presented and analyzed in detail. In addition to the two Hubbard operators, the operatorial basis comprises a third operator describing electronic transitions dressed by nearest-neighbor spin fluctuations. These latter, compared to charge and pair fluctuations, are assumed to be preeminent in the region of model-parameter space - small doping, low temperature and large on-site Coulomb repulsion - where one expects strong electronic correlations to dominate the physics of the system. This assumption and the consequent choice for the basic field, as well as the whole analytical approximation framework, have been validated through a comprehensive comparison with data for local and single-particle properties obtained by different numerical methods on varying all model parameters. The results systematically agree, both quantitatively and qualitatively, up to coincide in many cases. Many relevant features of the model, reflected by the numerical data, are exactly caught by the proposed solution and, in particular, the crossover between weak and intermediate-strong correlations as well as the shape of the occupied portion of the dispersion. A comprehensive comparison with other $n$-pole solutions is also reported in order to explore and possibly understand the reasons of such good performance.

19 pages, 8 figures, 27 panels

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Cited by in corpus (10)

• Mott insulators with boundary zeros
• Field-driven attosecond photoinjection dynamics in semiconductors
• Composite Operator Method analysis of the underdoped cuprates puzzle
• TR-ARPES Signal in Pumped Semiconductors within Dynamical Projective Operatorial Approach (DPOA)
• The composite operator method route to the 2D Hubbard model and the cuprates
• Single-particle properties of the Hubbard model in a novel three-pole approximation
• Quasi-particle propagation across semiconductor-Mott insulator interfaces
• Local properties of the t-J model in a two-pole approximation within COM
• Transmission through multiple Mott insulator - semiconductor wells
• COM(3p) solution of the 2D Hubbard model: momentum resolved quantities