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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| Format: | Journal Article |
| Language: | English |
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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 |
| _version_ | 1811697571434856448 |
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| author | Henley, Christopher L. Cheong, Siew Ann |
| author_facet | Henley, Christopher L. Cheong, Siew Ann |
| author_sort | Henley, Christopher L. |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T07:57:22Z |
| format | Journal Article |
| id | ntu-10356/90478 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:57:22Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | ntu-10356/904782023-02-28T19:33:12Z Operator-based truncation scheme based on the many-body fermion density matrix Henley, Christopher L. Cheong, Siew Ann DRNTU::Science::Physics::Atomic physics::Solid state physics 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. Published version 2009-05-12T04:07:31Z 2019-12-06T17:48:25Z 2009-05-12T04:07:31Z 2019-12-06T17:48:25Z 2004 2004 Journal Article 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. 0163-1829 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 10.1103/PhysRevB.69.075112 en Physical review B Physical Review B. @ copyright ©2004 The American Physical Society. The journal's website is located at http://www.aps.org/. 20 p. application/pdf |
| spellingShingle | DRNTU::Science::Physics::Atomic physics::Solid state physics Henley, Christopher L. Cheong, Siew Ann Operator-based truncation scheme based on the many-body fermion density matrix |
| title | Operator-based truncation scheme based on the many-body fermion density matrix |
| title_full | Operator-based truncation scheme based on the many-body fermion density matrix |
| title_fullStr | Operator-based truncation scheme based on the many-body fermion density matrix |
| title_full_unstemmed | Operator-based truncation scheme based on the many-body fermion density matrix |
| title_short | Operator-based truncation scheme based on the many-body fermion density matrix |
| title_sort | operator based truncation scheme based on the many body fermion density matrix |
| topic | DRNTU::Science::Physics::Atomic physics::Solid state physics |
| url | 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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