2018/06/30 by Yiyang Jia, J. J. M. Verbaarschot, Jacobus J. M. Verbaarschot · 19 citations
Mathematics · Physics and Astronomy · #Combinatorics #Cumulant #Enumeration #Fermion #Hamiltonian (control theory) #MAJORANA #Mathematical physics #Mathematics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chaos and dynamical systems #Quantum many-body systems #Quantum mechanics #Statistics #hep-th
paper · pdf · doi:10.1007/jhep11(2018)031
published in Journal of High Energy Physics 2018(11) (Springer Nature)
openalex publication_date 2018/11/01 · arxiv created 2018/11/20 · arxiv updated 2018/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract In this paper we explain the relation between the free energy of the SYK model for N Majorana fermions with a random q -body interaction and the moments of its spectral density. The high temperature expansion of the free energy gives the cumulants of the spectral density. Using that the cumulants are extensive we find the p dependence of the 1 /N 2 correction of the 2 p -th moments obtained in [1]. Conversely, the 1 /N 2 corrections to the moments give the correction (even q ) to the β 6 coefficient of the high temperature expansion of the free energy for arbitrary q . Our result agrees with the 1 /q 3 correction obtained by Tarnopolsky using a mean field expansion. These considerations also lead to a more powerful method for solving the moment problem and intersection-graph enumeration problems. We take advantage of this and push the moment calculation to 1 /N 3 order and find surprisingly simple enumeration identities for intersection graphs. The 1 /N 3 corrections to the moments, give corrections to the β 8 coefficient (for even q ) of the high temperature expansion of the free energy which have not been calculated before. Results for odd q , where the SYK “Hamiltonian” is the supercharge of a supersymmetric theory are discussed as well.