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Many-Body Density Matrices for Free Fermions

Siew-Ann Cheong·Christopher L. Henley
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Abstract

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 rho_B 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 G_ij = < c_i^+ c_j>, where c_i^+ 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[ sum_ij (log G(1 - G^{-1})_ij c_i^+ c_j]. Implications of such a result to Hilbert space truncation for real-space renormalization schemes is discussed.

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Siew-Ann Cheong, Christopher L. Henley. 2003-11-20. Many-Body Density Matrices for Free Fermions. https://arxiv.org/abs/cond-mat/0206196

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