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arXiv:cond-mat/9606185

A new field-theoretical formulation for the motion of an electron in a quenched disorder potential

Wolfgang Weller, Frank Stefani, M. Souleiman

Published Jun 25, 1996• 0 citations
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Abstract

Following a proposal by Aronov and Ioselevich, we express the Green functions (GF) of a noninteracting disordered Fermi system as a functional integral on a real time/frequency lattice. The normalizing denominator of this functional integral is equal to unity, because of identities satisfied by the GF. The GF can then be simply averaged with respect to the random disorder potential. We describe the fermionic fields not belonging to the external frequency by means of a bosonic auxiliary field g. The Hubbard-Stratonovich field Q is introduced only with respect to the fermionic fields for the external frequency.

DOI
10.48550/arxiv.cond-mat/9606185

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Following a proposal by Aronov and Ioselevich, we express the Green functions (GF) of a noninteracting disordered Fermi system as a functional integral on a real time/frequency lattice. The normalizing denominator of this functional integral is equal to unity, because of identities satisfied by the GF. The GF can then be simply averaged with respect to the random disorder potential. We describe the fermionic fields not belonging to the external frequency by means of a bosonic auxiliary field g. The Hubbard-Stratonovich field Q is introduced only with respect to the fermionic fields for the external frequency.
Abstract A real‐time finite‐temperature field theory on the Keldysh contour is used to describe the dynamics of an electron system within a random Hubbard model. The effective, i.e. quenched‐averaged, fermionic action under the functional integral is bosonized by introducing both a matrix field and an exchange field via Hubbard‐Stratonovich transformations. The resulting collective action permits the loop expansion, giving rise to a systematic approximation scheme. The saddle point and Gaussian fluctuations around it are calculated.
The disorder averaged single-particle Green's function of electrons subject to a time-dependent random potential with long-range spatial correlations is calculated by means of bosonization in arbitrary dimensions. For static disorder our method is equivalent with conventional perturbation theory based on the lowest order Born approximation. For dynamic disorder, however, we obtain a new non-perturbative expression for the average Green's function. Bosonization also provides a solid microscopic basis for the description of the quantum dynamics of an interacting many-body system via an effective stochastic model with Gaussian probability distribution.
Abstract Describing spin ↑ ‐electrons the particle number operators ni↓ are replaced under the functional integral directly by c‐numbers vi↓(t) using a δ‐functional instead of the Hubbard‐Stratonovich transformation. The Green function of the Hubbard model is thus exactly represented as an averaged Green function of electrons moving in a stochastic potential Uvi↓(t). The probability distribution for the stochastic process v ↓ containing the many body aspect and the information about the ↓‐electrons is determined. The vi↓(t) are only allowed to jump between 0 and 1 reflecting the property of Fermion particle number operators. This exact scheme can be interpreted as a dynamically generalized alloy analogy.