Describing systems of interacting fermions by boson models: exact mapping in arbitrary dimension and applications

Abstract

We develop a new method that allows us to map models of interacting fermions onto bosonic models describing collective excitations in an arbitrary dimension. This mapping becomes exact in the thermodynamic continuous time limit. The boson models can be written either in the form of a model of non-interacting bosons in a fluctuating auxiliary field or in the form of a superfield theory of interacting bosons. We show how one can study the latter version using perturbation theory. Using the developed diagrammatic technique we compared the first two orders of perturbation theory with the corresponding results for the original fermion model and found a perfect agreement. As concerns the former representation, we suggest a scheme that may be suitable for Monte Carlo simulations and demonstrate that it is free of the fermionic sign problem. We discuss in details the properties of the bosonic representation and argue that there should not be any obstacles preventing from an efficient computation.

Qualitative discussion of subsections IVc-IVe is modified. Figure 8 is added

References in corpus (6)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Supersymmetric low-energy theory and renormalization group for a clean Fermi gas with a repulsion in arbitrary dimensions
• Temperature dependence of the spin susceptibility of a clean Fermi gas with repulsion
• Exact bosonization for an interacting Fermi gas in arbitrary dimensions
• Cooper channel and the singularities in the thermodynamics of a Fermi liquid
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Cited by in corpus (8)

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• Topological Origin of the Fermion Sign Problem
• Effective Soft-Mode Theory of Strongly Interacting Fermions
• Low energy excitations and singular contributions in the thermodynamics of clean Fermi liquids
• Squashed entanglement in one-dimensional quantum matter
• Reckoning with the Mother of all non-Fermi liquids: alien bosonization vs predator holography
• Dimensional reduction of the Luttinger-Ward functional for spin-degenerate $D$-dimensional electron gases
• Anomalous Density-of-States Fluctuations in Two-Dimensional Clean Metals