Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models

Abstract

We compute the phase diagram of a $\text{U}(N{)}^2\times \text{O}(D)$ invariant fermionic planar matrix quantum mechanics [equivalently tensor or complex Sachdev-Ye-Kitaev (SYK) models] in the new large $D$ limit, dominated by melonic graphs. The Schwinger-Dyson equations can have two solutions describing either a high entropy, SYK black-hole-like phase, or a low entropy one with trivial IR behavior. In the strongly coupled region of the mass-temperature plane, there is a line of first order phase transitions between the high and low entropy phases. This line terminates at a new critical point which we study numerically in detail. The critical exponents are nonmean field and differ on the two sides of the transition. We also study purely bosonic unstable and stable melonic models. The former has a line of Kazakov critical points beyond which the Schwinger-Dyson equations do not have a consistent solution. Moreover, in both models the would-be SYK-like solution of the IR limit of the equations does not exist in the full theory.

14 pages, 5 figures, minor changes in v2

References in corpus (25)

• Thermoelectric transport in disordered metals without quasiparticles: the SYK models 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
• The Bulk Dual of SYK: Cubic Couplings
• The 1/N expansion of colored tensor models
• Quantum quench of the Sachdev-Ye-Kitaev Model
• Supersymmetric SYK model and random matrix theory
• Quantum Chaos and Holographic Tensor Models
• A Supersymmetric SYK-like Tensor Model
• Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
• The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories
• Random Matrices and Holographic Tensor Models
• Correlators in tensor models from character calculus
• Ward identities and combinatorics of rainbow tensor models
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• Echoes of chaos from string theory black holes
• Vector models and generalized SYK models
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• More on the New Large $D$ Limit of Matrix Models
• Conformality of $1/N$ corrections in SYK-like models
• Solvable Quantum Grassmann Matrices

Cited by in corpus (70)

• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Eternal traversable wormhole
• Notes on the complex Sachdev-Ye-Kitaev model
• An introduction to the SYK model
• Theory of a Planckian metal
• Quantum chaos transition in a two-site SYK model dual to an eternal traversable wormhole
• Notes on Melonic $O(N{)}^{q-1}$ Tensor Models
• Flat space holography and complex SYK
• Space-Time in the SYK Model
• The Large D Limit of Einstein's Equations
• Three Dimensional View of Arbitrary $q$ SYK models
• Prismatic Large $N$ Models for Bosonic Tensors
• 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
• Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments
• Pedagogical introduction to SYK model and 2D Dilaton Gravity
• Phases Of Melonic Quantum Mechanics
• Quantum Phase Transition in the Yukawa-SYK Model
• Subsystem Rényi Entropy of Thermal Ensembles for SYK-like models
• Cut and join operator ring in Aristotelian tensor model
• $T$-linear resistivity in models with local self-energy
• Excitation spectra of quantum matter without quasiparticles I: Sachdev-Ye-Kitaev models
• Traversable wormhole and Hawking-Page transition in coupled complex SYK models
• A Complex Fermionic Tensor Model in $d$ Dimensions
• SYK-like tensor quantum mechanics with $\mathrm{Sp}(N)$ symmetry
• Phase transition and chaos in charged SYK model
• Notes on Matrix Models
• Supersymmetric SYK Model with Global Symmetry
• When things stop falling, chaos is suppressed
• Large $N$ limit of irreducible tensor models: $O(N)$ rank-$3$ tensors with mixed permutation symmetry
• Complex Sachdev-Ye-Kitaev model in the double scaling limit
• Phase diagram of the spin-1/2 Yukawa-SYK model: Non-Fermi liquid, insulator, and superconductor
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• From Kronecker to tableau pseudo-characters in tensor models
• On Melonic Supertensor Models
• Phases of $\mathcal{N}=2$ Sachdev-Ye-Kitaev models
• Invariant Operators, Orthogonal Bases and Correlators in General Tensor Models
• Strongly coupled quantum phonon fluid in a solvable model
• Tensor and Matrix models: a one-night stand or a lifetime romance?
• 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
• Quantum chaos and phase transition in the Yukawa-SYK model
• $Q$-Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model
• Chaos in Three-dimensional Higher Spin Gravity
• Near Conformal Perturbation Theory in SYK Type Models
• Thermalization in different phases of charged SYK model
• Spontaneous Symmetry Breaking in Tensor Theories
• Melonic Turbulence
• Holography, quantum complexity and quantum chaos in different models
• Matching partition functions of deformed JT gravity and the cSYK model
• Lattice models for Non-Fermi Liquids with Tunable Transport Scalings
• Dynamics and Charge Fluctuations in Large-q Sachdev-Ye-Kitaev Lattices
• Thermodynamic and Real-time Dynamic Properties of Complex Sachdev-Ye-Kitaev Model
• Quantum discontinuity fixed point and renormalization group flow of the SYK model
• Quantum Chaos, Thermodynamics and Black Hole Microstates in the mass deformed SYK model
• Bipartite Sachdev-Ye Models with Read-Saleur Symmetries
• Thermodynamics and dynamics of coupled complex SYK models
• Sign-Problem-Free Variant of Complex Sachdev-Ye-Kitaev Model
• Scaling limits of complex Sachdev-Ye-Kitaev models and holographic geometry
• Exotic quantum statistics and thermodynamics from a number-conserving theory of Majorana fermions
• Superlinear Hall angle and carrier mobility from non-Boltzmann magnetotransport in the spatially disordered Yukawa-Sachdev-Ye-Kitaev model on a square lattice
• High-frequency transport and zero-sound in an array of SYK quantum dots
• 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
• Strange Metal to Insulator Transitions in the Lowest Landau Level
• Chiral symmetry breaking generalizes in tensor theories
• Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models
• Janus van der Waals equations for real molecules with two-sided phase transitions
• Gauging the complex SYK model