SYK model with an extra diagonal perturbation: phase transition in the eigenvalue spectrum

Abstract

We study the SYK model with an extra constant source, i.e. a constant matrix or equivalently a diagonal matrix with only one non-zero entry ${\lambda }_1$. By using methods from analytic combinatorics, we find exact expressions for the moments of this model. We further prove that the spectrum of this model can have a gap when ${\lambda }_1>{\lambda }_1^c$, thus exhibiting a phase transition in ${\lambda }_1$. In this case, a single isolated eigenvalue splits off from SYK's eigenvalues distribution. We located this single eigenvalue by analyzing the singular behavior of a supercritical functional composition scheme. In certain limit our results recover the ones of random matrices with non-zero mean entries.

arXiv comment22 pages (1 appendix and with references included), 7 figures

References in corpus (10)

• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Holographic metals and the fractionalized Fermi liquid
• Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
• Towards a full solution of the large N double-scaled SYK model
• Phase Transition in the Density of States of Quantum Spin Glasses
• Non-ergodic extended states in the SYK model
• Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$
• Large $N$ expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs
• Solving the Frustrated Spherical Model with q-Polynomials
• On the algebraic area of lattice walks and the Hofstadter model

Cited by in corpus (2)

• SYK Model with global symmetries in the double scaling limit
• Composition schemes: q-enumerations and phase transitions