Research output: Contribution to journal › Article

**Multivaluedness of the Luttinger-Ward functional in the fermionic and bosonic system with replicas.** / Kim, Aaram J.; Sacksteder, Vincent.

Research output: Contribution to journal › Article

Kim, AJ & Sacksteder, V 2020, 'Multivaluedness of the Luttinger-Ward functional in the fermionic and bosonic system with replicas', *Physical Review B*, vol. 101, no. 11, 115146. https://doi.org/10.1103/PhysRevB.101.115146

Kim, A. J., & Sacksteder, V. (2020). Multivaluedness of the Luttinger-Ward functional in the fermionic and bosonic system with replicas. *Physical Review B*, *101*(11), [115146]. https://doi.org/10.1103/PhysRevB.101.115146

Kim AJ, Sacksteder V. Multivaluedness of the Luttinger-Ward functional in the fermionic and bosonic system with replicas. Physical Review B. 2020 Mar 15;101(11). 115146. https://doi.org/10.1103/PhysRevB.101.115146

@article{ca8e8c3dac4648ce809569eb8c925dd0,

title = "Multivaluedness of the Luttinger-Ward functional in the fermionic and bosonic system with replicas",

abstract = "We study the properties of the Luttinger-Ward functional (LWF) in a simplified Hubbard-type model without time or spatial dimensions, but with N identical replicas located on a single site. The simplicity of this (0+0)d model permits an exact solution for all N and for both bosonic and fermionic statistics. We show that fermionic statistics are directly linked to the fact that multiple values of the noninteracting Green's function G0 map to the same value of the interacting Green's function G; that is, the mapping G0{\^a}†G is noninjective. This implies that with fermionic statistics the (0+0)dN-replica model has a multiply valued LWF. The number of LWF values in the fermionic model increases proportionally to the number of replicas N, while in the bosonic model the LWF has a single value regardless of N. We also discuss the formal connection between the N-replica model and the (0+1)d Hubbard atom which was used in previous studies of LWF's multivaluedness.",

author = "Kim, {Aaram J.} and Vincent Sacksteder",

year = "2020",

month = mar,

day = "15",

doi = "10.1103/PhysRevB.101.115146",

language = "English",

volume = "101",

journal = "Physical Review B (Condensed Matter and Materials Physics)",

issn = "1098-0121",

publisher = "American Physical Society",

number = "11",

}

TY - JOUR

T1 - Multivaluedness of the Luttinger-Ward functional in the fermionic and bosonic system with replicas

AU - Kim, Aaram J.

AU - Sacksteder, Vincent

PY - 2020/3/15

Y1 - 2020/3/15

N2 - We study the properties of the Luttinger-Ward functional (LWF) in a simplified Hubbard-type model without time or spatial dimensions, but with N identical replicas located on a single site. The simplicity of this (0+0)d model permits an exact solution for all N and for both bosonic and fermionic statistics. We show that fermionic statistics are directly linked to the fact that multiple values of the noninteracting Green's function G0 map to the same value of the interacting Green's function G; that is, the mapping G0â†G is noninjective. This implies that with fermionic statistics the (0+0)dN-replica model has a multiply valued LWF. The number of LWF values in the fermionic model increases proportionally to the number of replicas N, while in the bosonic model the LWF has a single value regardless of N. We also discuss the formal connection between the N-replica model and the (0+1)d Hubbard atom which was used in previous studies of LWF's multivaluedness.

AB - We study the properties of the Luttinger-Ward functional (LWF) in a simplified Hubbard-type model without time or spatial dimensions, but with N identical replicas located on a single site. The simplicity of this (0+0)d model permits an exact solution for all N and for both bosonic and fermionic statistics. We show that fermionic statistics are directly linked to the fact that multiple values of the noninteracting Green's function G0 map to the same value of the interacting Green's function G; that is, the mapping G0â†G is noninjective. This implies that with fermionic statistics the (0+0)dN-replica model has a multiply valued LWF. The number of LWF values in the fermionic model increases proportionally to the number of replicas N, while in the bosonic model the LWF has a single value regardless of N. We also discuss the formal connection between the N-replica model and the (0+1)d Hubbard atom which was used in previous studies of LWF's multivaluedness.

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U2 - 10.1103/PhysRevB.101.115146

DO - 10.1103/PhysRevB.101.115146

M3 - Article

AN - SCOPUS:85083249338

VL - 101

JO - Physical Review B (Condensed Matter and Materials Physics)

JF - Physical Review B (Condensed Matter and Materials Physics)

SN - 1098-0121

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ER -

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