Many-body density matrices for free fermions

• Main Authors: Henley, Christopher L., Cheong, Siew Ann
• Format: Article
• Language: English
• Published: 2009
• Subjects: DRNTU::Science::Physics::Atomic physics::Solid state physics
• Online Access: https://hdl.handle.net/10356/90932; http://hdl.handle.net/10220/4593
• Institution: Nanyang Technological University

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.