Classification of the quantum chaos in colored Sachdev-Ye-Kitaev models

Abstract

The random matrix theory (RMT) can be used to classify both topological phases of matter and quantum chaos. We develop a systematic and transformative RMT to classify the quantum chaos in the colored Sachdev-Ye-Kitaev (SYK) model first introduced by Gross and Rosenhaus. Here we focus on the 2-colored case and 4-colored case with balanced number of Majorana fermion $N$. By identifying the maximal symmetries, the independent parity conservation sectors, the minimum (irreducible) Hilbert space, and especially the relevant anti-unitary and unitary operators, we show that the color degree of freedoms lead to novel quantum chaotic behaviours. When $N$ is odd, different symmetry operators need to be constructed to make the classifications complete. The 2-colored case only show 3-fold Wigner-Dyson way, and the 4-colored case show 10-fold generalized Wigner-Dyson way which may also have non-trivial edge exponents. We also study 2- and 4-colored hybrid SYK models which display many salient quantum chaotic features hidden in the corresponding pure SYK models. These features motivate us to develop a systematic RMT to study the energy level statistics of 2 or 4 un-correlated random matrix ensembles. The exact diagonalizations are performed to study both the bulk energy level statistics and the edge exponents and find excellent agreements with our exact maximal symmetry classifications. Our complete and systematic methods can be easily extended to study the generic imbalanced cases. They may be transferred to the classifications of colored tensor models, quantum chromodynamics with pairings across different colors, quantum black holes and interacting symmetry protected (or enriched) topological phases.

arXiv comment20 pages, 9 figures, 4 tables, REVTEX, Accepted by Phys. Rev. D

References in corpus (51)

• Topological Insulators
• Topological insulators and superconductors
• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Zoo of quantum-topological phases of matter
• Topological phases of fermions in one dimension
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Black Holes and Random Matrices
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Bekenstein-Hawking Entropy and Strange Metals
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• Fermionic Localization of the Schwarzian Theory
• 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
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Solving the Schwarzian via the Conformal Bootstrap
• Quantum Fluctuations of a Nearly Critical Heisenberg Spin Glass
• Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States
• Numerical study of fermion and boson models with infinite-range random interactions
• Putting competing orders in their place near the Mott transition
• The complete $1/N$ expansion of a SYK--like tensor model
• An introduction to the SYK model
• Digital Quantum Simulation of Minimal AdS/CFT
• Supersymmetric SYK model and random matrix theory
• Statistical mechanics of a two-dimensional black hole
• Creating and probing the Sachdev-Ye-Kitaev model with ultracold gases: Towards experimental studies of quantum gravity
• Random Matrix Theory of a Chaotic Andreev Quantum Dot
• Approximating the Sachdev-Ye-Kitaev model with Majorana wires
• Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
• Black hole on a chip: proposal for a physical realization of the SYK model in a solid-state system
• Spectra of Operators in Large $N$ Tensor Models
• Majorana Fermions, Exact Mapping between Quantum Impurity Fixed Points with four bulk Fermion species, and Solution of the ``Unitarity Puzzle''
• Joint probability densities of level spacing ratios in random matrices
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Goldstone and Higgs modes of photons inside a cavity
• On Emery-Kivelson line and universality of Wilson ratio of spin anisotropic Kondo model
• Abelian bosonization approach to quantum impurity problems
• Duality, Magnetic space group and their applications to quantum phases and phase transitions on bipartite lattices in several experimental systems
• Stressed Cooper pairing in QCD at high isospin density: effective Lagrangian and random matrix theory
• Banks-Casher-type relation for the BCS gap at high density
• Quantum phases, Supersolids and quantum phase transitions of interacting bosons in frustrated lattices
• Characterizing symmetry breaking patterns in a lattice by dual vortex degree of freedoms
• Parity oscillations and photon correlation functions in the $Z_2/U(1)$ Dicke model at a finite number of atoms or qubits

Cited by in corpus (8)

• Probing symmetries of quantum many-body systems through gap ratio statistics
• Many-body localization in a fragmented Hilbert space
• Periodic Table of SYK and supersymmetric SYK
• Rotating Black Holes in AdS, Extremality and Chaos
• Superposition and higher-order spacing ratios in random matrix theory with application to complex systems
• Level statistics of the one-dimensional ionic Hubbard model
• Universal scaling of higher-order spacing ratios in Gaussian random matrices
• A bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics