Sachdev-Ye-Kitaev model


In condensed matter physics and black hole physics, the Sachdev-Ye-Kitaev model commonly known as SYK model is an exactly solvable model initially proposed by Subir Sachdev and his graduate student Jinwu Ye and later modified by Alexei Kitaev to the present commonly used form. The model is believed to bring insights into the understanding of strongly correlated materials and it also has a close relation with the discrete model of AdS/CFT, and Fermionic code. The model is amenable to digital quantum simulation, with pioneering experiments implemented in a NMR setting.

SYK model

Let be an integer and and even integer such that, consider a set of Majorana Fermions which are Fermion operators satisfy conditions: Hermitian ; Clifford relation. Choosing a random variable such that the expectation satisfy: ; and , Then the SYK model is defined as
Note that sometimes, an extra normalization factor will be added.
The more famous model is when, then the model becomes
notice that here the factor is added for coincidence with the usually used form.