TY - JOUR

T1 - Absence of Luttinger’s theorem for fermions with power-law Green functions

AU - Limtragool, Kridsanaphong

AU - Leong, Zhidong

AU - Phillips, Philip W.

N1 - Funding Information:
We thank NSF DMR-1461952 for partial funding of this project. KL is supported by the Department of Physics at the University of Illinois and a scholarship from the Ministry of Science and Technology, Royal Thai Government. ZL is supported by the Department of Physics at the University of Illinois and a scholarship from the Agency of Science, Technology and Research, Singapore.
Publisher Copyright:
Copyright K. Limtragool et al.

PY - 2018/11

Y1 - 2018/11

N2 - We investigate the validity of Luttinger’s theorem (or Luttinger sum rule) in two scale-invariant fermionic models. We find that, in general, Luttinger’s theorem does not hold in a system of fermions with power-law Green functions which do not necessarily preserve particle-hole symmetry. However, Ref. [1,2] showed that Luttinger liquids, another scale-invariant fermionic model, respect Luttinger’s theorem. To understand the difference, we examine the spinless Luttinger liquid model. We find two properties which make the Luttinger sum rule valid in this model: particle-hole symmetry and ImG(ω = 0, -∞) = 0. We conjecture that these two properties represent sufficient, but not necessary, conditions for the validity of the Luttinger sum rule in condensed matter systems.

AB - We investigate the validity of Luttinger’s theorem (or Luttinger sum rule) in two scale-invariant fermionic models. We find that, in general, Luttinger’s theorem does not hold in a system of fermions with power-law Green functions which do not necessarily preserve particle-hole symmetry. However, Ref. [1,2] showed that Luttinger liquids, another scale-invariant fermionic model, respect Luttinger’s theorem. To understand the difference, we examine the spinless Luttinger liquid model. We find two properties which make the Luttinger sum rule valid in this model: particle-hole symmetry and ImG(ω = 0, -∞) = 0. We conjecture that these two properties represent sufficient, but not necessary, conditions for the validity of the Luttinger sum rule in condensed matter systems.

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U2 - 10.21468/SciPostPhys.5.5.049

DO - 10.21468/SciPostPhys.5.5.049

M3 - Article

AN - SCOPUS:85078323144

VL - 5

JO - SciPost Physics

JF - SciPost Physics

SN - 2542-4653

IS - 5

M1 - 049

ER -