eCommons

 

Many-body fermion density matrices

Other Titles

Abstract

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).

Journal / Series

Volume & Issue

Description

Ph.D. thesis, submitted January 2006, supervisor Prof. Christopher Henley.

Sponsorship

Supported by the U.S. National Science Foundation.

Date Issued

2008-10-23T22:02:19Z

Publisher

Keywords

Location

Effective Date

Expiration Date

Sector

Employer

Union

Union Local

NAICS

Number of Workers

Committee Chair

Committee Co-Chair

Committee Member

Degree Discipline

Degree Name

Degree Level

Doctor of Philosophy

Related Version

Related DOI

Related To

Related Part

Based on Related Item

Has Other Format(s)

bibid: 8295286
bibid: 6026344

Part of Related Item

Related To

Related Publication(s)

Link(s) to Related Publication(s)

References

Link(s) to Reference(s)

Previously Published As

Government Document

ISBN

ISMN

ISSN

Other Identifiers

Rights

Rights URI

Types

dissertation or thesis

Accessibility Feature

Accessibility Hazard

Accessibility Summary

Link(s) to Catalog Record