Many-body density matrices on a two-dimensional square lattice : noninteracting and strongly interacting spinless 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/10356/90479; http://hdl.handle.net/10220/4602
• Institution: Nanyang Technological University

The reduced density matrix of an interacting system can be used as the basis for a truncation scheme, or in an unbiased method to discover the strongest kind of correlation in the ground state. In this paper, we investigate the structure of the many-body fermion density matrix of a small cluster in a square lattice. The cluster density matrix is evaluated numerically over a set of finite systems, subject to non-square periodic boundary conditions given by the lattice vectors R1 = (R1x, R1y) and R2 = (R2x, R2y). We then approximate the infinite-system cluster density-matrix spectrum by averaging the finite-system cluster density matrix (i) over degeneracies in the ground state, and orientations of the system relative to the cluster, to ensure it has the proper point-group symmetry; and (ii) over various twist boundary conditions to reduce finite size effects. We then compare the eigenvalue structure of the averaged cluster density matrix for noninteracting and strongly interacting spinless fermions, as a function of the filling fraction n¯, and discuss whether it can be approximated as being built up from a truncated set of single-particle operators.