Simple Models of Many-Fermion Systems

J. Zhang, W. Pötz

Generalized many-fermion versions of the independent-boson model with fixed or variable fermion number are solved exactly. In particular, the linear-response characteristics of these systems are discussed. Exact results for physical quantities, such as the partition function and the two-time correlation function for single-fermion operators, as needed in the Kubo formula, are given and discussed. These nontrivial models may serve as simple model systems for interacting many-particle systems and as a testing ground for approximation schemes for more complex coupled many-particle systems.

Masatoshi Imada

The negative sign problem is a serious difficulty with most existing Monte Carlo methods of evaluating fermion systems of greater than one-dimension because it makes the computation of physical variables practically impossible. A simple and general averaging method is proposed for many-fermion systems. This method is completely free of the negative sign problem. The efficiency and convergence are verified in the Feynman's path integral calculations of a few simple models.

Nouredine Zettili

João Costa, Pedro Ribeiro, Andrea De Luca

We analyze the effects of various forms of noise on one-dimensional systems of noninteracting fermions. In the strong noise limit, we demonstrate, under mild assumptions, that the statistics of the fermionic correlation matrix in the thermodynamic limit follow a universal form described by the recently introduced quantum simple symmetric exclusion process (QSSEP). For charge transport, we show that QSSEP, along with all models in its universality class, shares the same large deviation function for the transferred charge as the classical SSEP model. The method we introduce to derive this result relies on a gaugelike invariance associated with the choice of the bond where the current is measured. This approach enables the explicit calculation of the cumulant-generating function for both QSSEP and SSEP and establishes an exact correspondence between them. These analytical findings are validated by extensive numerical simulations. Our results establish that a wide range of noisy free-fermionic models share the same QSSEP universality class and show that their transport properties are essentially classical.