2005/08/31 by Siew-Ann Cheong, Siew Ann Cheong, Christopher L. Henley
Physics and Astronomy · #Advanced Condensed Matter Physics #Boundary value problem #Cluster (spacecraft) #Density matrix #Eigenvalues and eigenvectors #Fermion #Ground state #Ising model #Lattice (music) #Matrix (chemical analysis) #Periodic boundary conditions #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum mechanics #Square lattice #Wave function #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.74.165121
14 pages in RevTeX4 format, 8 figures
arxiv created 2006/07/22 · openalex publication_date 2006/10/31 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 nonsquare periodic boundary conditions given by the lattice vectors R1\ensuremath≡(R1x,R1y) and R2\ensuremath≡(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.