Hermitian boson mapping and finite truncation

Abstract

Starting from a general, microscopic fermion-to-boson mapping that preserves Hermitian conjugation, we discuss truncations of the boson Fock space basis. We give conditions under which the exact boson images of finite fermion operators are also finite (e.g., a 1+2-body fermion Hamiltonian is mapped to a 1+2-body boson Hamiltonian) in the truncated basis. For the most general case, where the image is not necessarily exactly finite, we discuss how to make practical and controlled approximations. 03.65.Ca, 21.60.-n Typeset using REVTEX 1 Pairwise correlations are often important in describing the physics of many-fermion systems. The classic paradigm is the BCS theory of superconductivity [1], where the wavefunction is dominated by Cooper pairs which have electrons coupled up to zero linear momentum and spin; these boson-like pairs condense into a coherent wavefunction. Another example is the phenomenological Interacting Boson Model (IBM) for nuclei [2], where many states an

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