Many-Body Density Matrices for Free Fermions

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Building upon an analytical technique introduced by Chung and Peschel [M. Chung and I. Peschel, Phys. Rev. B 64, art. 064412 (2001)], we calculated the density matrix rhoB of a finite block of B sites within an infinite system of free spinless fermions. In terms of the block Green function matrix G (whose elements are Gᵢj = < cᵢ+ cⱼ>, where cᵢ+ and cⱼ are fermion creation and annihilation operators acting on sites i and j within the block respectively), the density matrix can be written as rhoB = det(1 - G) exp[sumᵢj (log G(1 - G⁻¹)ᵢj cᵢ+ cⱼ]. Implications of such a result to Hilbert space truncation for real-space renormalization schemes is discussed.