Optical conductivity of the two-dimensional Hubbard model: Vertex corrections, emergent Galilean invariance, and the accuracy of the single-site dynamical mean field approximation

Journal Article · 29 August 2022 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.106.085142 · OSTI ID:1979809

Mu, Anqi  ^[1]; Sun, Zhiyuan  ^[2]; Millis, Andrew J. ^[3]

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1. Columbia Univ., New York, NY (United States); OSTI
2. Harvard Univ., Cambridge, MA (United States)
3. Columbia Univ., New York, NY (United States); Flatiron Institute, New York, NY (United States)

We compute the frequency-dependent conductivity of the two-dimensional square lattice Hubbard model at zero temperature as a function of density to second order in the interaction strength, and compare the results to the predictions of single-site dynamical mean field theory computed at the same order. We find that despite the neglect of vertex corrections, the single-site dynamical mean field approximation produces semiquantitatively accurate results for most carrier concentrations, but fails qualitatively for the nearly empty or nearly filled band cases where the model exhibits an emergent Galilean invariance. The DMFT approximation also becomes qualitatively inaccurate very near half filling if nesting is important.

• Research Organization: Columbia Univ., New York, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0018426
• OSTI ID: 1979809
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 8 Vol. 106; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English