Operator-based truncation scheme based on the many-body fermion density matrix
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 b...
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Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
2009
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Online Access: | https://hdl.handle.net/10356/90478 http://hdl.handle.net/10220/4601 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 |
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Institution: | Nanyang Technological University |
Language: | English |
Summary: | 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. |
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