Phases Of Melonic Quantum Mechanics

Frank Ferrari , Fidel I. Schaposnik Massolo (1)

1 IHES - Institut des Hautes Études Scientifiques

We explore in detail properties of two melonic quantum mechanical theories which can be formulated either as fermionic matrix quantum mechanics in the new large D limit, or as disordered models. Both models have a mass parameter m and the transition from the perturbative large m region to the strongly coupled “black-hole” small m region is associated with several interesting phenomena. One model, with U(n)2 symmetry and equivalent to complex Sachdev-Ye-Kitaev, has a line of first-order phase transitions terminating, for a strictly positive temperature, at a critical point having nontrivial, nonmean-field critical exponents for standard thermodynamical quantities. Quasinormal frequencies, as well as Lyapunov exponents associated with out-of-time-ordered four-point functions, are also singular at the critical point, leading to interesting new critical exponents. The other model, with reduced U(n) symmetry, has a quantum critical point at strictly zero temperature and positive critical mass m*. For 0

Mots clés: String theory; quantum gravity; gauge/gravity duality; temperature: 0; scaling: dimension; fixed point: infrared; n-point function: 4; critical phenomena; quantum mechanics; spontaneous symmetry breaking; two-point function; thermodynamical; strong coupling; black hole; Euclidean; flow

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique Générale [physics.gen-ph]

Frank Ferrari, Fidel I. Schaposnik Massolo. Phases Of Melonic Quantum Mechanics. Physical Review D, 2019, 100 (2), pp.026007. ⟨10.1103/PhysRevD.100.026007⟩. ⟨hal-02080722⟩