Many-body fermion density matrices
MetadataShow full item record
This four-part thesis is on the reduced many-body density matrices of systems of noninteracting and interacting spinless fermions, and the exact solution of ladder models of interacting spinless fermions. In the first part (Chapters 2 and 3), we derived an exact formula relating the density matrix and Green function for a cluster of sites within a system of noninteracting spinless fermions in any dimensions. Based on the thermodynamic form of the cluster density matrix in this exact formula, we proposed a truncation scheme in which the new Hilbert space is built from a truncated set of spinless fermion operators. In the second part (Chapter 4), we studied various finite size effects in the cluster density-matrix spectra, and looked at how these can be reduced or eliminated using the method of twist boundary conditions averaging, for finite two-dimensional systems of noninteracting and interacting spinless fermions. We also checked the feasibility of the operator-based truncation scheme for interacting systems. In the third part (Chapters 5, 6, and 8), we developed a systematic and unbiased machinery, based on the decomposition of the density matrix of two disjoint clusters $a$ and $b$, into a sum of products of an operator on cluster $a$ and an operator on cluster $b$, to extract the various quantum-mechanical correlations, from a numerical exact-diagonalization ground-state wave function. This machinery was applied to explore the ground-state phase diagram of the extended Hubbard ladder of spinless fermions with correlated hops (which are next-nearest-neighbor hops that occur in the presence of occupied nearest neighbors).
Ph.D. thesis, submitted January 2006, supervisor Prof. Christopher Henley.
Supported by the U.S. National Science Foundation.
Doctor of Philosophy
Has other format(s)
bibid: 8295286bibid: 6026344
dissertation or thesis