In
condensed matter physics and
black hole physics, the Sachdev–Ye–Kitaev (SYK) model is an exactly solvable model initially proposed by
Subir Sachdev and Jinwu Ye,[1] and later modified by
Alexei Kitaev to the present commonly used form.[2][3] 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. Many condensed matter systems, such as quantum dot coupled to topological superconducting wires,[4] graphene flake with irregular boundary,[5] and kagome optical lattice with impurities,[6] are proposed to be modeled by it. Some variants of the model are amenable to digital quantum simulation,[7] with pioneering experiments implemented in
nuclear magnetic resonance.[8]
Model
Let be an integer and an even integer such that , and consider a set of
Majorana fermions which are fermion operators satisfying conditions:
Hermitian ;
Clifford relation .
Let be random variables whose expectations satisfy:
;
.
Then the SYK model is defined as
.
Note that sometimes an extra normalization factor is included.
The most famous model is when :
,
where the factor is included to coincide with the most popular form.