2010/01/31 by K. B. Efetov, C. Pépin, H. Meier +1
Mathematics · Physics and Astronomy · #Algorithm #Boson #Cold Atom Physics and Bose-Einstein Condensates #Computation #Computer science #Diagrammatic reasoning #Dimension (graph theory) #Fermion #Mathematics #Perturbation theory (quantum mechanics) #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum and electron transport phenomena #Quantum mechanics #Representation (politics) #Statistical physics #Theoretical physics #cond-mat.quant-gas #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.82.235120
published as Phys. Rev. B 82, 235120 (2010) · Qualitative discussion of subsections IVc-IVe is modified. Figure 8 is added
arxiv created 2010/09/26 · openalex publication_date 2010/12/14 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We develop a method that allows us to map models of interacting fermions onto bosonic models describing collective excitations in an arbitrary dimension. We present arguments that this mapping may become exact in the thermodynamic limit in the presence of a bath. The boson models can be written either in the form of a model of noninteracting bosons in a fluctuating auxiliary Hubbard-Stratonovich field or in the form of a superfield theory of interacting bosons. We show how one can study the latter version within the perturbation theory. Using a diagrammatic technique developed for the boson model we compare the first two orders of the perturbation theory with the corresponding results for the original fermion model and find a perfect agreement. As concerns the former representation, we suggest a scheme that may be suitable for Monte Carlo simulations. We demonstrate both analytically and numerically that the partition function of the boson model in the auxiliary Hubbard-Stratonovich field is, in contrast to the fermion model, always positive and thus the boson model can be suitable for the Monte Carlo routine. At the same time, our arguments showing the equivalence of the boson and fermion models in the thermodynamic limit are not completely rigorous and it is still to be investigated numerically how accurate the boson model can approximate the original fermion one.