Phases Of Melonic Quantum Mechanics
Frank Ferrari, Fidel I. Schaposnik Massolo
TL;DR
This paper investigates two melonic quantum mechanical models, revealing complex phase transitions, critical phenomena, and IR fixed points, with detailed analysis of their thermodynamics, critical exponents, and symmetry breaking.
Contribution
It provides a detailed analysis of phase transitions and critical behavior in two melonic quantum models, including new critical exponents and IR fixed points, with pedagogical derivations.
Findings
First-order phase transition line with a critical point and non-mean-field exponents
Singular behavior of quasi-normal frequencies and Lyapunov exponents at criticality
Existence of a zero-temperature quantum critical point with spontaneous scale invariance breaking
Abstract
We explore in detail the properties of two melonic quantum mechanical theories which can be formulated either as fermionic matrix quantum mechanics in the new large limit, or as disordered models. Both models have a mass parameter and the transition from the perturbative large region to the strongly coupled "black-hole" small region is associated with several interesting phenomena. One model, with symmetry and equivalent to complex SYK, has a line of first-order phase transitions terminating, for a strictly positive temperature, at a critical point having non-trivial, non-mean-field critical exponents for standard thermodynamical quantities. Quasi-normal 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,…
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