HEP Theory Journal Club

SYK Lindbladian

Tokiro Numasawa

Tokyo University

We study the Lindbladian dynamics of the Sachdev-Ye-Kitaev (SYK) model, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. Here, the linear jump operators are non-random while the quadratic jump operators are sampled from a Gaussian distribution. In the limit of large N, where N is the number of Majorana fermion operators, and also in the limit of large N and M, where M is the number of jump operators, the SYK Lindbladians are analytically tractable, and we obtain their stationary Green’s functions, from which we can read off the decay rate. For finite N, we also study the distribution of the eigenvalues of the SYK Lindbladians. Then, we consider the time evolution of the dissipative form factor, which quantifies the average overlap between the initial and time-evolved density matrices as an open quantum generalization of the Loschmidt echo. We find that the dissipative form factor exhibits dynamical quantum phase transitions. We analytically demonstrate a discontinuous dynamical phase transition in the limit of a large number of fermion flavors, which is formally akin to the thermal phase transition in the two-coupled SYK model between the black-hole and wormhole phases. We also find continuous dynamical phase transitions that do not have counterparts in the two-coupled SYK model. Furthermore, we numerically show that signatures of the dynamical quantum phase transitions remain to appear even in the finite number of fermion flavors. Finally I will comment on possible connections to de Sitter wormholes. This talk is based on the papers arxiv:2112.13489 and arxiv:2210.04093.