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.

arXiv comment135 pages, 50 figures, 2 tables. Minor corrections and updated list of references in v3. Title changed to match published version

References in corpus (110)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Black holes and the butterfly effect
• Chaos in AdS${}_2$ holography
• The Spectrum in the Sachdev-Ye-Kitaev Model
• An Investigation of AdS${}_2$ Backreaction and Holography
• Black Holes and Random Matrices
• Quantum Field Theory in the Large N Limit: a review
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Bekenstein-Hawking Entropy and Strange Metals
• Multiple Shocks
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Holographic metals and the fractionalized Fermi liquid
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Fermionic Localization of the Schwarzian Theory
• Critical behavior of colored tensor models in the large N limit
• Diving into traversable wormholes
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Colored Tensor Models - a Review
• A Generalization of Sachdev-Ye-Kitaev
• The complete 1/N expansion of colored tensor models in arbitrary dimension
• Non-Fermi liquid regime of a doped Mott insulator
• Colored Group Field Theory
• Quantum Fluctuations of a Nearly Critical Heisenberg Spin Glass
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Solvable model for a dynamical quantum phase transition from fast to slow scrambling
• The large D limit of General Relativity
• Eternal traversable wormhole
• A semiclassical ramp in SYK and in gravity
• Bi-Local Holography in the SYK Model
• More on Supersymmetric and 2d Analogs of the SYK Model
• Overscreened multi-channel SU(N) Kondo model : large-N solution and Conformal Field Theory
• The 1/N expansion of colored tensor models in arbitrary dimension
• The Bulk Dual of SYK: Cubic Couplings
• The 1/N expansion of colored tensor models
• Towards a full solution of the large N double-scaled SYK model
• Mean-Field Theory of a Quantum Heisenberg Spin Glass
• Quantum quench of the Sachdev-Ye-Kitaev Model
• All point correlation functions in SYK
• Supersymmetric SYK model and random matrix theory
• Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
• Quantum Chaos and Holographic Tensor Models
• Models of AdS_2 Backreaction and Holography
• $O(N)$ Random Tensor Models
• Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
• A Supersymmetric SYK-like Tensor Model
• 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 $\epsilon$
• Notes on Melonic $O(N{)}^{q-1}$ Tensor Models
• Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models
• Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains
• Universal low temperature theory of charged black holes with AdS${}_2$ horizons
• Spectra of Operators in Large $N$ Tensor Models
• Dispersive SYK model: band structure and quantum chaos
• Transition from overscreening to underscreening in the multichannel Kondo model: exact solution at large N
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• Random Matrices and Holographic Tensor Models
• Reconstructing the thermal Green functions at real times from those at imaginary times
• The 1/N expansion of multi-orientable random tensor models
• Multi-orientable Group Field Theory
• Space-Time in the SYK Model
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev Model
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Three Dimensional View of Arbitrary $q$ SYK models
• Quenched equals annealed at leading order in the colored SYK model
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• Prismatic Large $N$ Models for Bosonic Tensors
• Critical exponents can be different on the two sides of a transition: A generic mechanism
• Towards a bulk description of higher spin SYK
• 2PI effective action for the SYK model and tensor field theories
• Thouless time for mass-deformed SYK
• Symmetry Breaking in Coupled SYK or Tensor Models
• Echoes of chaos from string theory black holes
• The $1/N$ expansion of the symmetric traceless and the antisymmetric tensor models in rank three
• Spectra of Eigenstates in Fermionic Tensor Quantum Mechanics
• 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
• Contrasting SYK-like Models
• Diffusion in higher dimensional SYK model with complex fermions
• Tensorial Gross-Neveu models
• The $1/N$ expansion of tensor models with two symmetric tensors
• Supersymmetric SYK models
• Towards the Holographic Dual of N = 2 SYK
• Towards a Finite-$N$ Hologram
• A Complex Fermionic Tensor Model in $d$ Dimensions
• SYK-like tensor quantum mechanics with $\mathrm{Sp}(N)$ symmetry
• On large $q$ expansion in the Sachdev-Ye-Kitaev model
• Multi-critical behaviour of 4-dimensional tensor models up to order 6
• Supersymmetric SYK Model with Global Symmetry
• $\mathcal{N}=2$ SYK model in the superspace formalism
• When things stop falling, chaos is suppressed
• More on the New Large $D$ Limit of Matrix Models
• Large $N$ limit of irreducible tensor models: $O(N)$ rank-$3$ tensors with mixed permutation symmetry
• Spectrum of Majorana Quantum Mechanics with $O(4{)}^3$ Symmetry
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• On Melonic Supertensor Models
• Introduction to the Keldysh formalism and applications to time-dependent density-functional theory
• Higher melonic theories
• Tensor and Matrix models: a one-night stand or a lifetime romance?
• Exact Solution of a Strongly Coupled Gauge Theory in 0+1 Dimensions
• Melonic Turbulence
• Complete Solution of a Gauged Tensor Model
• The Analytic Renormalization Group

Cited by in corpus (30)

• The Large D Limit of Einstein's Equations
• Excitation spectra of quantum matter without quasiparticles I: Sachdev-Ye-Kitaev models
• Complex Sachdev-Ye-Kitaev model in the double scaling limit
• Phases of $\mathcal{N}=2$ Sachdev-Ye-Kitaev models
• Revisited functional renormalization group approach for random matrices in the large-$N$ limit
• Holographic boundary states and dimensionally-reduced braneworld spacetimes
• Melonic Dominance in Subchromatic Sextic Tensor Models
• Non-Hermitian quantum system generated from two coupled Sachdev-Ye-Kitaev models
• Phase diagram of a two-site coupled complex Sachdev-Ye-Kitaev model
• The shared universality of charged black holes and the many many-body SYK model
• Flowing in discrete gravity models and Ward identities: A review
• Quantum Correction to Chaos in Schwarzian Theory
• Matching partition functions of deformed JT gravity and the cSYK model
• Dynamics and Charge Fluctuations in Large-q Sachdev-Ye-Kitaev Lattices
• Excitation Transmission through a non-Hermitian traversable wormhole
• Quantum discontinuity fixed point and renormalization group flow of the SYK model
• Thermodynamic and Real-time Dynamic Properties of Complex Sachdev-Ye-Kitaev Model
• Current-induced inverse symmetry breaking and asymmetric critical phenomena at current-driven tricritical point
• Sign-Problem-Free Variant of Complex Sachdev-Ye-Kitaev Model
• Thermodynamics and dynamics of coupled complex SYK models
• Quantum Chaos, Thermodynamics and Black Hole Microstates in the mass deformed SYK model
• Scaling limits of complex Sachdev-Ye-Kitaev models and holographic geometry
• 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
• Superlinear Hall angle and carrier mobility from non-Boltzmann magnetotransport in the spatially disordered Yukawa-Sachdev-Ye-Kitaev model on a square lattice
• Tensor Field Theories: Renormalization and Random Geometry
• Multiple scaling limits of $\mathrm{U}(N{)}^2\times \mathrm{O}(D)$ multi-matrix models
• Strange Metal to Insulator Transitions in the Lowest Landau Level
• Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models
• Gauging the complex SYK model