Phases of melonic quantum mechanics

Abstract

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 UðnÞ 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 UðnÞ symmetry, has a quantum critical point at strictly zero temperature and positive critical mass m à . For 0 < m < m à , it flows to a new gapless IR fixed point, for which the standard scale invariance is spontaneously broken by the appearance of distinct scaling dimensions Δ þ and Δ − for the Euclidean two-point function when t → þ∞ and t → −∞ respectively. We provide several detailed and pedagogical derivations, including rigorous proofs or simplified arguments for some results that were already known in the literature.

Hints of unitarity at large N in the O(N )3 tensor field theory

“…Tensor models were initially studied in zero dimension in the context of quantum gravity and random geometry [3,[14][15][16][17]. They were then studied in one dimension [18][19][20][21][22][23][24][25][26][27][28][29][30] (see also [4,31] for reviews) as a generalization of the Sachdev-Ye-Kitaev model [32][33][34][35][36][37] without quenched disorder.…”

On the chaos bound in rotating black holes

“…Several aspects of this system can be capture by a 2-dimensional Einstein-dilation theory, and this has generated a lot of research within the framework of NAdS 2 /NCFT 1 and related areas. See, for instance, [14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Quantum chaos, thermodynamics and black hole microstates in the mass deformed SYK model

“…Recently the quantum chaotic property was also studied in a variety of deformations of the SYK model [13,14,[33][34][35][36][37][38][39][40]. Among these developments in [13] the authors considered a deformation of the SYK Hamiltonian by a random mass term and found that the quantum Lyapunov exponent decreases as the mass parameter is increased.…”

“…Also, the connection between chaos and the thermalization property of the system implies that one cannot see whether the system is chaotic or not just by looking thermodinamic quantities such as the free energy [46]. Nevertheless, there are some examples [14,34] where we have multiple evidences that they are indeed correlated. It would be interesting to ask what kind of additional properties of a model can relate the chaotic/integrable transition and the Hawking-Page like transition indirectly, which will define an interesting class of theories.…”