Constraint Quantization of Slave-Particle Theories

Details Constraint Quantization of Slave-Particle Theories Constraint Quantization of Slave-Particle Theories

1996-07-08

arxiv.org/abs/cond-mat/9607058v1

Physica B 230-232 (1997), 451

Physics

Condensed Matter

LATEX, 5 pages

Scientific paper

10.1016/S0921-4526(96)00611-4

We start from the Barnes-Coleman slave-particle description, where the Hubbard operators $X$ are decomposed into a product of fermionic ($f_{\alpha}$) and bosonic ($b$) operators. The quantum mechanical constraint $b^{\dagger} b + \sum_{\alpha} f_{\alpha}^{\dagger} f_{\alpha} = 1$ is treated within the framework of Dirac's method for the quantization of classical constrained systems. This leads to modified algebraic properties of the fundamental operators: $b b^{\dagger} b = b$, $f_{\alpha} f_{\beta}^{\dagger} f_{\gamma} = \delta_{\alpha \beta} f_{\gamma}$ and $ f_{\alpha} b^{\dagger}= 0 $. Thereby the algebra of the $X$-operators is preserved exactly on the operator level. Matrix representations of the above algebra are constructed and a resolvent-like perturbation theory for the single-impurity Anderson model is developed.

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