Related papers: Combinatorial study of graphs arising from the Sac…
The Sachdev-Ye-Kitaev (SYK) model provides an uncommon example of a chaotic theory that can be analysed analytically. In the deep infrared limit, the original model has an emergent conformal (reparametrisation) symmetry that is broken both…
A strong interaction is known to exist between edge-colored graphs (which encode PL pseudo-manifolds of arbitrary dimension) and random tensor models (as a possible approach to the study of Quantum Gravity). The key tool is the {\it…
The 0+1-d Sachdev-Ye-Kitaev (SYK) fermionic model attracts nowadays a wide spread interest of the Condensed Matter community, as a benchmark toy model for strong electron correlation and non Fermi Liquid behavior. It is exactly solvable in…
Several condensed-matter platforms have been proposed recently to realize the Sachdev-Ye-Kitaev (SYK) model in their low-energy limit. In these proposed realizations, the characteristic SYK behavior is expected to occur under certain…
We investigate the spectral form factor of the sparse Sachdev-Ye-Kitaev model. We use numerical methods to establish that at intermediate times the connected part of the spectral form factor is the dominant one. These connected…
The Sachdev-Ye-Kitaev (SYK) model is a concrete model for non-Fermi Liquid with maximally chaotic behavior in $0+1$-$d$. In order to gain some insights into real materials in higher dimensions where fermions could hop between different…
Quantum chaos is one of the distinctive features of the Sachdev-Ye-Kitaev (SYK) model, $N$ Majorana fermions in $0+1$ dimensions with infinite-range two-body interactions, which is attracting a lot of interest as a toy model for holography.…
Some generalizations of the Sachdev-Ye-Kitaev (SYK) model and different patterns of their reparametrization symmetry breaking are discussed. The analysis of such (pseudo)holographic systems relates their generalized one-dimensional…
The random matrix theory (RMT) can be used to classify both topological phases of matter and quantum chaos. We develop a systematic and transformative RMT to classify the quantum chaos in the colored Sachdev-Ye-Kitaev (SYK) model first…
We study a bipartite version of the Sachdev-Ye-Kitaev (SYK) model. We show that the model remains solvable in the limit of large-$N$ in the same sense as the original model if the ratio of both flavors is kept finite. The scaling dimensions…
Entanglement is one of the most important concepts in quantum physics. We review recent progress in understanding the quantum entanglement in many-body systems using large-$N$ solvable models: the Sachdev-Ye-Kitaev (SYK) model and its…
We study the chaos exponent of some variants of the Sachdev-Ye-Kitaev (SYK) model, namely, the $\Ns=1$ supersymmetry (SUSY)-SYK model and its sibling, the $(N|M)$-SYK model which is not supersymmetric in general, for arbitrary interaction…
Binomial Cayley graphs are obtained by considering the binomial coefficient of the weight function of a given Cayley graph and a natural number. We introduce these objects and study two families: one associated with symmetric groups and the…
A colloquium style review of the connections between the Sachdev-Ye-Kitaev model and strange metals without quasiparticles, and between the SYK model and the quantum properties of black holes. Along with other insights, this connection has…
In this article we are introducing combinatorial spectra of graphs, this is a generalization of $H$-Hamiltonian spectra. The main motivation was to made from $H$-Hamiltonian spectra an operation and develop some algebra in this field. An…
We study a description of the large N limit of the Sachdev-Ye-Kitaev (SYK) model in terms of quantum mechanics without quenched disorder. Instead of random couplings, we introduce massive scalar fields coupled to fermions, and study a small…
A proof of Sharkovsky's Theorem is given. It is shown how this proof naturally generalizes to looking at maps on graphs and to Sharkovsky-type theorems for these maps. The paper is written at an elementary level and is meant as an…
Colouring problems arising from group-based constructions provide a natural link between combinatorics and algebra, particularly in the study of Cayley graphs and Latin squares. We introduce the notion of colouring bijections of finite…
Understanding the emergence of complex correlations in strongly interacting systems remains a fundamental challenge in quantum many-body physics. One fruitful approach is to develop solvable toy models that encapsulate universal properties…
The paper investigates connections between abstract polytopes and properly edge colored graphs. Given any finite n-edge-colored n-regular graph G, we associate to G a simple abstract polytope P_G of rank n, called the colorful polytope of…