We study a generalization of ‘‘Yukawa models’’ in which Majorana fermions, interacting via all-to-all random couplings as in the Sachdev-Ye-Kitaev (SYK) model, are parametrically coupled to disordered bosonic degrees of freedom described by a quantum $p-\text{spin}$ model. The latter has its own nontrivial dynamics leading to quantum paramagnetic (or liquid) and glassy phases. At low temperatures, this setup results in SYK behavior within each metastable state of a rugged bosonic free-energy landscape, the effective fermionic couplings being different for each metastable state. We show that the boson-fermion coupling enhances the stability of the quantum spin-glass phase and strongly modifies the imaginary-time Green’s functions of both sets of degrees of freedom. In particular, in the quantum spin-glass phase, the imaginary-time dynamics is turned from a fast exponential decay characteristic of a gapped phase into a much slower dynamics. In the quantum paramagnetic phase, on the other hand, the fermions' imaginary-time dynamics get strongly modified, and the critical SYK behavior is washed away.

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• Disordered systems
• Glassy systems
• Many-body techniques
• Mean field theory
• Path-integral methods
• Replica methods
• Sachdev-Ye-Kitaev model