Many-body density matrices for free fermions - Henley, Christopher L. (2009)
Building upon an analytical technique introduced by Chung and Peschel [Phys. Rev. B 64, 064412 (2001)], we calculated the many-body density matrix ρB of a finite block of B sites within an infinite system of free spinless fermions in arbitrary dimensions. In terms of the block Green function matrix G (whose elements are Gīj=〈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 ρB=det(1-G)exp(∑ij[ln G(1-G)-1]ijci†cj). Our results suggest that Hilbert space truncation schemes should retain the states created by a subset of the ci†’s (in any combination), rather than selecting eigenvectors of ρB independently based on the eigenvalue.