Phases Of Melonic Quantum Mechanics

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 $D$ 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 $\mathrm{U}(n{)}^2$ 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, with reduced $\mathrm{U}(n)$ symmetry, has a quantum critical point at strictly zero temperature and positive critical mass $m_{\ast }$. For $0<m<m_{\ast }$, 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 ${\Delta }_{+}$ and ${\Delta }_{-}$ for the Euclidean two-point function when $t\to +\infty$ and $t\to -\infty$ respectively. We provide several detailed and pedagogical derivations, including rigorous proofs or simplified arguments for some results that were already known in the literature.

135 pages, 50 figures, 2 tables. Minor corrections and updated list of references in v3. Title changed to match published version

References in corpus (27)

• An Investigation of AdS${}_2$ Backreaction and Holography
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• A Generalization of Sachdev-Ye-Kitaev
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• More on Supersymmetric and 2d Analogs of the SYK Model
• The 1/N expansion of colored tensor models
• Quantum quench of the Sachdev-Ye-Kitaev Model
• All point correlation functions in SYK
• Quantum chaos transition in a two-site SYK model dual to an eternal traversable wormhole
• Three Dimensional View of the SYK/AdS Duality
• Bosonic Tensor Models at Large $N$ and Small $\epsilon$
• Universal low temperature theory of charged black holes with AdS${}_2$ horizons
• Dispersive SYK model: band structure and quantum chaos
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• Symmetry Breaking in Coupled SYK or Tensor Models
• A note on the SYK model with complex fermions
• On Large $N$ Limit of Symmetric Traceless Tensor Models
• Thermal out-of-time-order correlators, KMS relations, and spectral functions
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Diffusion in higher dimensional SYK model with complex fermions
• The $1/N$ expansion of tensor models with two symmetric tensors
• Towards a Finite-$N$ Hologram
• Introduction to the Keldysh formalism and applications to time-dependent density-functional theory

Cited by in corpus (3)

• Non-Hermitian quantum system generated from two coupled Sachdev-Ye-Kitaev models
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• The quantum $p$-spin glass model: A user manual for holographers