Bipolaron formed through electron-hole excitation

Wu, Chen-Huan

doi:10.1088/1402-4896/abca59

Cited by 1 publication

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“…As we investigated in Ref. [23], the particle-hole excitation is essential for the formation of bipolaron, and to leading order the density-density correlation (bosonic self-energy) vanishes for the multi-loop bosonic planar diagram in particle-hole channel, as long as the loop number is ≥ 3 (there does not exists such two loop diagram since three (or other odd number of) fermionic propagators cannot connected to one single point in a planar diagram). Thus the only case for nonzero bosonic self-energy (in particle-hole channel) is the one loop diagram.…”

Section: Three-point Boson Mode and The Related Verticesmentioning

confidence: 99%

Electronic properties of the boson mode in a three-point fermion loop and the emergent SYK physics

Wu¹

2020

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We investigate the electronic properties of the boson mode in a three-point fermion loop. In this framwork, the single-particle excitation and the many-body local (in imaginary time and momentum space) field effects are investigated in IR or UV limits with the density fluctuation induced by external potential (or bosonic frequency). The (partly) cancellation effects of the bosonic density-density correlation in a multiloop particle-hole diagram with even Green's functions and a one-loop particle-hole diagram with odd Green's functions are studied. In the limit of vanishing effect of external potential, which is equivalent to UV limit of the fermionic frequency, the conserving approximation can be applied together with the Luttinger-Ward analysis, in which case the anomalous contribution to the fermion self-energy or the expectation value of many-body interaction term, which is g 2 ∆ † ∆ (g is the irreducible particle-particle vertex and ∆ is the boson field operator), vanishes, and results in a Hartree-Fock type momentum-and frequency-independent fermion self-energy. The correlator ∆ † ∆ is positive which can be obtained through the local moment sum rule of dynamical susceptibility. In the long-wavelength limit with low-energy (IR limit of boson mode), the irreducible particle-particle vertex can be replaced by the bare one, i.e., the RPA expression, where ∆ † ∆ = ∆ † ∆ and the electronic compressibility then becomes zero even at finite temperature and with finite chemical potential. We also verify that the GG 0 G 0 approach, where only the first Green's function be dressed, is valid in obtaining the self-consistent relation (between single fermion property and that of the boson mode) and the sum rules, even with the bare interaction and beyond the long-wavelength limit. While the GGG approach with a reducible vertex has been proved be a bad approximation perviously in obtaining sum rules (and it breaks conservation laws), we found it is useful to obtain the bosonic mass or chemical potential in IR limit. Some conclusions about IR asymptotic behaviors of SYK model are also applied in this paper, to deal with the fermions with a marginal fermi-liquid scaling Green's function, where we found the collective mode cannot be obtained in this case by solving the singularities of dynamical susceptibility. The effect of strong quantum fluctuations induced by particle-hole excitation near fermi surface are not been considered here.

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Section: Three-point Boson Mode and The Related Verticesmentioning

confidence: 99%