True vs false Fermi surfaces in the Pseudogap regime and their transformation with doping and temperature in the Hubbard Model
Abstract
Exact diagrammatic quantum Monte Carlo (DiagMC) results for the nearest-neighbor Hubbard model motivate a closer study of the pseudogap. Using the improved two-particle self-consistent approach (TPSC+), we analyze Energy (EDC) and Momentum Distribution Curves (MDC) simultaneously. We show that Fermi-liquid terminology breaks down in the pseudogap regime, requiring a distinction between true and false Fermi surfaces and zero-energy quasiparticle (ZEQ) lines. A false Fermi surface has a momentum-space spectral maximum but a frequency-space depression at zero energy, while a false ZEQ line violates the standard quasiparticle condition ∂ Σ'(k,ω)/∂ ω|ω=0<0.The pseudogap is driven by critical thermal spin fluctuations, which occur in two dimensions because of the Mermin-Wagner theorem. Commensurate fluctuations first open an antinodal pseudogap, leaving true Fermi arcs. With decreasing temperature, the Fermi surface evolves into hole- and electron-like false Fermi surfaces. Incommensurate fluctuations generate hot spots near the diagonal, where the pseudogap persists to the quantum critical point (QCP), whereas at kAN it disappears before the QCP doping. There, the spectrum has two precursor antiferromagnetic (AFM) bands, both in the unoccupied (ω>0) region. We benchmark TPSC+ against DiagMC results for the Matsubara spectral proxy −Im[𝒢(k,iπT)]/π. TPSC+ underestimates pseudogap suppression in the strong-interaction regime, reproducing DiagMC behavior at lower temperatures or doping. This proxy is equivalent to the spectral function with thermal broadening η=πT, which obscures features when πT is not the smallest energy scale. Using A(k,0), we find that hole-like Fermi surfaces emerge at any interaction strength at low temperature, even at weak coupling.
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BibTeX
@misc{vilk2026true,
title = {{True vs false Fermi surfaces in the Pseudogap regime and their transformation with doping and temperature in the Hubbard Model}},
author = {Y. M. Vilk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12339},
eprint = {2610.12339},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12339},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - True vs false Fermi surfaces in the Pseudogap regime and their transformation with doping and temperature in the Hubbard Model
AU - Y. M. Vilk
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12339
UR - https://arxiv.org/abs/2610.12339
AB - Exact diagrammatic quantum Monte Carlo (DiagMC) results for the nearest-neighbor Hubbard model motivate a closer study of the pseudogap. Using the improved two-particle self-consistent approach (TPSC+), we analyze Energy (EDC) and Momentum Distribution Curves (MDC) simultaneously. We show that Fermi-liquid terminology breaks down in the pseudogap regime, requiring a distinction between true and false Fermi surfaces and zero-energy quasiparticle (ZEQ) lines. A false Fermi surface has a momentum-space spectral maximum but a frequency-space depression at zero energy, while a false ZEQ line violates the standard quasiparticle condition ∂ Σ'(k,ω)/∂ ω|_ω=0<0.The pseudogap is driven by critical thermal spin fluctuations, which occur in two dimensions because of the Mermin-Wagner theorem. Commensurate fluctuations first open an antinodal pseudogap, leaving true Fermi arcs. With decreasing temperature, the Fermi surface evolves into hole- and electron-like false Fermi surfaces. Incommensurate fluctuations generate hot spots near the diagonal, where the pseudogap persists to the quantum critical point (QCP), whereas at k_AN it disappears before the QCP doping. There, the spectrum has two precursor antiferromagnetic (AFM) bands, both in the unoccupied (ω>0) region. We benchmark TPSC+ against DiagMC results for the Matsubara spectral proxy −Im[𝒢(k,iπT)]/π. TPSC+ underestimates pseudogap suppression in the strong-interaction regime, reproducing DiagMC behavior at lower temperatures or doping. This proxy is equivalent to the spectral function with thermal broadening η=πT, which obscures features when πT is not the smallest energy scale. Using A(k,0), we find that hole-like Fermi surfaces emerge at any interaction strength at low temperature, even at weak coupling.
ER -