  In [S. A. Cheong and C. L. Henley, cond-mat/0206196 (2002)], we found that
the many-particle eigenvalues and eigenstates of the many-body density matrix
$\rho_B$ of a block of $B$ sites cut out from an infinite chain of
noninteracting spinless fermions can all be constructed out of the one-particle
eigenvalues and one-particle eigenstates respectively. In this paper we
developed a statistical-mechanical analogy between the density matrix
eigenstates and the many-body states of a system of noninteracting fermions.
Each density matrix eigenstate corresponds to a particular set of occupation of
single-particle pseudo-energy levels, and the density matrix eigenstate with
the largest weight, having the structure of a Fermi sea ground state,
unambiguously defines a pseudo-Fermi level. We then outlined the main ideas
behind an operator-based truncation of the density matrix eigenstates, where
single-particle pseudo-energy levels far away from the pseudo-Fermi level are
removed as degrees of freedom. We report numerical evidence for scaling
behaviours in the single-particle pseudo-energy spectrum for different block
sizes $B$ and different filling fractions $\nbar$. With the aid of these
scaling relations, which tells us that the block size $B$ plays the role of an
inverse temperature in the statistical-mechanical description of the density
matrix eigenstates and eigenvalues, we looked into the performance of our
operator-based truncation scheme in minimizing the discarded density matrix
weight and the error in calculating the dispersion relation for elementary
excitations. This performance was compared against that of the traditional
density matrix-based truncation scheme, as well as against a operator-based
plane wave truncation scheme, and found to be very satisfactory.
