Year: 2004
Type: article
Abstract: Building upon an analytical technique introduced by Chung and Peschel [Phys. Rev. B 64, 064412 (2001)], we calculated the many-body density matrix ${\ensuremath{\rho}}_{B}$ 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 ${G}_{\ifmmode \bar{\imath}\else \={\i}\fi{}j}=〈{c}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{c}_{j}〉,$ where ${c}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}$ 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 ${\ensuremath{\rho}}_{B}=\mathrm{det}(1\ensuremath{-}G)\mathrm{exp}({\ensuremath{\sum}}_{\mathrm{ij}}[\mathrm{ln}G(1\ensuremath{-}{G)}^{\ensuremath{-}1}{]}_{\mathrm{ij}}{c}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{c}_{j}).$ Our results suggest that Hilbert space truncation schemes should retain the states created by a subset of the ${c}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}$'s (in any combination), rather than selecting eigenvectors of ${\ensuremath{\rho}}_{B}$ independently based on the eigenvalue.
Source: Physical Review B
Authors: Siew-Ann Cheong, Christopher L. Henley
Institution: Cornell University
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2076085919