Quantifying the fragility of unprotected quadratic band crossing points
| Autor: | Stephan Hesselmann, Carsten Honerkamp, Thomas C. Lang, Stefan Wessel |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Physics
Strongly Correlated Electrons (cond-mat.str-el) Quantum Monte Carlo Fermi level FOS: Physical sciences 02 engineering and technology Fermion 021001 nanoscience & nanotechnology 01 natural sciences Renormalization Brillouin zone symbols.namesake Condensed Matter - Strongly Correlated Electrons Lattice (order) Quantum mechanics 0103 physical sciences Density of states symbols Condensed Matter::Strongly Correlated Electrons Perturbation theory (quantum mechanics) 010306 general physics 0210 nano-technology |
| DOI: | 10.48550/arxiv.1912.06585 |
| Popis: | We examine a basic lattice model of interacting fermions that exhibits quadratic band crossing points (QBCPs) in the non-interacting limit. In particular, we consider spinless fermions on the honeycomb lattice with nearest neighbor hopping $t$ and third-nearest neighbor hopping $t''$, which exhibits fine-tuned QBCPs at the corners of the Brillouin zone for ${t'' = t/2}$. In this situation, the density of states remains finite at the Fermi level of the half-filled band and repulsive nearest-neighbor interactions $V$ lead to a charge-density-wave (CDW) instability at infinitesimally small $V$ in the random-phase approximation or mean-field theory. We examine the fragility of the QBCPs against dispersion renormalizations in the ${t\mbox{-}t''\mbox{-}V}$ model using perturbation theory, and find that the $t''$-value needed for the QBCPs increases with $V$ due to the hopping renormalization. However, the instability toward CDW formation always requires a nonzero threshold interaction strength, i.e., one cannot fine-tune $t''$ to recover the QBCPs in the interacting system. These perturbative arguments are supported by quantum Monte Carlo simulations for which we carefully compare the corresponding threshold scales at and beyond the QBCP fine-tuning point. From this analysis, we thus gain a quantitative microscopic understanding of the fragility of the QBCPs in this basic interacting fermion system. Comment: 9 pages, 10 figures |
| Databáze: | OpenAIRE |
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