dc.contributor.author | Karlsson, Daniel | |
dc.contributor.author | van Leeuwen, Robert | |
dc.date.accessioned | 2016-10-13T06:24:25Z | |
dc.date.available | 2016-10-13T06:24:25Z | |
dc.date.issued | 2016 | |
dc.identifier.citation | Karlsson, D., & van Leeuwen, R. (2016). Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule. <i>Physical Review B</i>, <i>94</i>(12), Article 125124. <a href="https://doi.org/10.1103/PhysRevB.94.125124" target="_blank">https://doi.org/10.1103/PhysRevB.94.125124</a> | |
dc.identifier.other | CONVID_26259067 | |
dc.identifier.other | TUTKAID_71417 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/51609 | |
dc.description.abstract | We consider a general class of approximations which guarantees the conservation of particle number in
many-body perturbation theory. To do this we extend the concept of derivability for the self-energy to a
larger class of diagrammatic terms in which only some of the Green’s function lines contain the fully dressed
Green’s function G. We call the corresponding approximations for partially derivable. A special subclass of
such approximations, which are gauge invariant, is obtained by dressing loops in the diagrammatic expansion of
consistently with G. These approximations are number conserving but do not have to fulfill other conservation
laws, such as the conservation of energy and momentum. From our formalism we can easily deduce whether
commonly used approximations will fulfill the continuity equation, which implies particle number conservation.
We further show how the concept of partial derivability plays an important role in the derivation of a generalized
sum rule for the particle number, which reduces to the Luttinger-Ward theorem in the case of a homogeneous
electron gas, and the Friedel sum rule in the case of the Anderson model. To do this we need to ensure that
the Green’s function has certain complex analytic properties, which can be guaranteed if the spectral function
is positive-semidefinite. The latter property can be ensured for a subset of partially -derivable approximations
for the self-energy, namely those that can be constructed from squares of so-called half diagrams. For the case
in which the analytic requirements are not fulfilled we highlight a number of subtle issues related to branch cuts,
pole structure, and multivaluedness. We also show that various schemes of computing the particle number are
consistent for particle number conserving approximations. | |
dc.language.iso | eng | |
dc.publisher | American Physical Society | |
dc.relation.ispartofseries | Physical Review B | |
dc.subject.other | many-body perturbation theory | |
dc.subject.other | approximations | |
dc.subject.other | particle number conservation | |
dc.subject.other | Green's function | |
dc.title | Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-201610104318 | |
dc.contributor.laitos | Fysiikan laitos | fi |
dc.contributor.laitos | Department of Physics | en |
dc.contributor.oppiaine | Nanoscience Center | fi |
dc.contributor.oppiaine | Nanoscience Center | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.date.updated | 2016-10-10T15:15:07Z | |
dc.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
dc.description.reviewstatus | peerReviewed | |
dc.relation.issn | 2469-9950 | |
dc.relation.numberinseries | 12 | |
dc.relation.volume | 94 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © 2016 American Physical Society. Published in this repository with the kind permission of the publisher. | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 267839 | |
dc.relation.doi | 10.1103/PhysRevB.94.125124 | |
dc.relation.funder | Suomen Akatemia | fi |
dc.relation.funder | Academy of Finland | en |
jyx.fundingprogram | Akatemiahanke, SA | fi |
jyx.fundingprogram | Academy Project, AoF | en |
jyx.fundinginformation | D.K. and R.v.L. would like to thank the Academy of Finland for support under Project No. 267839. | |
dc.type.okm | A1 | |