Operator-based truncation scheme based on the many-body fermion density matrix

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Operator-based truncation scheme based on the many-body fermion density matrix

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dc.contributor.author Cheong, Siew Ann
dc.contributor.author Henley, Christopher L.
dc.date.accessioned 2009-05-12T04:07:31Z
dc.date.available 2009-05-12T04:07:31Z
dc.date.copyright 2004
dc.date.issued 2009-05-12T04:07:31Z
dc.identifier.citation Cheong, S. A., & Henley, C. L. (2004). Operator-based truncation scheme based on the many-body fermion density matrix. Physical Review B., 69(7), 1-20.
dc.identifier.issn 0163-1829
dc.identifier.uri http://hdl.handle.net/10220/4601
dc.description.abstract In an earlier work [S. A. Cheong and C. L. Henley, preceding paper], we derived an exact formula for the many-body density matrix ρ B of a block of B sites cut out from an infinite chain of noninteracting spinless fermions, and found that the many-particle eigenvalues and igenstates of ρ B can all be constructed out of the one-particle eigenvalues and one-particle eigenstates, respectively. In this paper we improved upon this understanding, and 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. Based on this analogy, we 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 behaviors in the single-particle pseudo-energy spectrum for different block sizes B and different filling fractions n. With the aid of these scaling relations, which tell 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 an operator-based plane-wave truncation scheme, and found to be very satisfactory.
dc.format.extent 20 p.
dc.language.iso en
dc.relation.ispartofseries Physical review B
dc.rights Physical Review B. @ copyright ©2004 The American Physical Society. The journal's website is located at http://www.aps.org/.
dc.subject DRNTU::Science::Physics::Atomic physics::Solid state physics
dc.title Operator-based truncation scheme based on the many-body fermion density matrix
dc.type Journal Article
dc.identifier.openurl http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ISI_WOS_XML&id=doi:&genre=&isbn=&issn=1098-0121&date=2004&volume=69&issue=7&spage=&epage=&aulast=Cheong&aufirst=%20SA&auinit=SA&title=PHYSICAL%20REVIEW%20B&atitle=Operator%2Dbased%20truncation%20scheme%20based%20on%20the%20many%2Dbody%20fermion%20density%20matrix
dc.identifier.doi http://dx.doi.org/10.1103/PhysRevB.69.075112
dc.description.version Published version

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