Many-body density matrices for free fermions
Many-body density matrices for free fermions
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DOI：
10.1103/physrevb.69.075111
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发表时间：
2002-06
影响因子：
3.7
通讯作者：
S. Cheong;C. Henley
中科院分区：
文献类型：
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作者：
S. Cheong;C. Henley
以 Chung 和 Peschel 引入的分析技术为基础 [Phys. Rev. B 64, 064412 (2001)]，我们计算了任意维度的无限自由无自旋费米子系统内 B 位点有限块的多体密度矩阵 ${\ensuremath{\rho}}_{B}$。就块格林函数矩阵 G 而言（其元素为 ${G}_{\ifmmode \bar{\imath}\else \={\i}\fi{}j}=〈{c}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{c}_{j}〉,$ 其中 ${c}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}$ 和${c}_{j}$ 分别是作用于块内 i 和 j 位置的费米子创建和湮灭算子），密度矩阵可以写为${\ensuremath{\rho}}_{B}=\mathrm{det}(1\ensuremath{-}G)\mathrm{exp}({\ensuremath{\sum}}_{\mathrm{ij}}[\mathrm{ln }G(1\ensuremath{-}{G)}^{\ensuremath{-}1}{]}_{\mathrm{ij}}{c}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{c}_{j})。$我们的结果表明希尔伯特空间截断方案应该保留 ${c}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}$ 的子集（任何组合）创建的状态，而不是根据特征值独立选择 ${\ensuremath{\rho}}_{B}$ 的特征向量。
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.