Many-body density matrices for free fermions

Building upon an analytical technique introduced by Chung and Peschel [Phys. Rev. B 64, 064412 (2001)], we calculated the many-body density matrix rho(B) 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 G((i) over barj)=<c(i)(dagger)c(j)>, where c(i)(dagger) and c(j) are fermion creation and annihilation operators acting on sites i and j within the block, respectively), the density matrix can be written as rho(B)=det(1-G)exp(Sigma(ij)[ln G(1-G)(-1)](ij)c(i)(dagger)c(j)). Our results suggest that Hilbert space truncation schemes should retain the states created by a subset of the c(i)(dagger)'s (in any combination), rather than selecting eigenvectors of rho(B) independently based on the eigenvalue.