Chaos on the hypercube

Abstract

We analyze the spectral properties of a $d$-dimensional HyperCubic (HC) lattice model originally introduced by Parisi. The U(1) gauge links of this model give rise to a magnetic flux of constant magnitude $\varphi$ but random orientation through the faces of the hypercube. The HC model, which also can be written as a model of $2d$ interacting Majorana fermions, has a spectral flow that is reminiscent of the Maldacena-Qi (MQ) model, and its spectrum at $\varphi =0$, actually coincides with the coupling term of the MQ model. As was already shown by Parisi, at leading order in $1/d$ , the spectral density of this model is given by the density function of the Q-Hermite polynomials, which is also the spectral density of the double-scaled Sachdev-Ye-Kitaev model. Parisi demonstrated this by mapping the moments of the HC model to $Q$-weighted sums on chord diagrams. We point out that the subleading moments of the HC model can also be mapped to weighted sums on chord diagrams, in a manner that descends from the leading moments. The HC model has a magnetic inversion symmetry that depends on both the magnitude and the orientation of the magnetic flux through the faces of the hypercube. The spectrum for fixed quantum number of this symmetry exhibits a transition from regular spectra at $\varphi =0$ to chaotic spectra with spectral statistics given by the Gaussian Unitary Ensembles (GUE) for larger values of $\varphi$. For small magnetic flux, the ground state is gapped and is close to a Thermofield Double (TFD) state.

References in corpus (50)

• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Eternal Black Holes in AdS
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• Bekenstein-Hawking Entropy and Strange Metals
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
• Random Matrix Theory and Chiral Symmetry in QCD
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Quantum Fluctuations of a Nearly Critical Heisenberg Spin Glass
• Eternal traversable wormhole
• A semiclassical ramp in SYK and in gravity
• Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States
• Notes on the complex Sachdev-Ye-Kitaev model
• Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
• Towards a full solution of the large N double-scaled SYK model
• Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
• Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction
• Quantum chaos transition in a two-site SYK model dual to an eternal traversable wormhole
• Phase Transition in the Density of States of Quantum Spin Glasses
• Universal fluctuations in spectra of the lattice Dirac operator
• Quantum ergodicity in the SYK model
• How to Build the Thermofield Double State
• Review of the k-Body Embedded Ensembles of Gaussian Random Matrices
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Sparse Sachdev-Ye-Kitaev model, quantum chaos and gravity duals
• Quantum Group and Magnetic Translations. Bethe-Ansatz Solution for Azbel-Hofstadter Problem
• Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev Model
• Spectral Statistics of the Two-Body Random Ensemble Revisited
• Thouless time for mass-deformed SYK
• Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
• Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$
• Contrasting SYK-like Models
• Spectral Fluctuations in the Sachdev-Ye-Kitaev Model
• Statistical properties of the spectrum of the QCD Dirac operator at low energy
• $D$-dimensional Arrays of Josephson Junctions, Spin Glasses and $q$-deformed Harmonic Oscillators
• A Sparse Model of Quantum Holography
• Decay of a Thermofield-Double State in Chaotic Quantum Systems
• Majorana Fermion Quantum Mechanics for Higher Rank Tensors
• Dirac Spectra of 2-dimensional QCD-like theories
• Large $N$ expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs
• Replica Theory and Large D Josephson Junction Hypercubic Models
• Solving the Frustrated Spherical Model with q-Polynomials
• Shift of Symmetries of Naive Fermions in QCD-like Lattice Theories
• Area versus Length Distribution for Closed Random Walks
• Magnetic translation symmetry on the lattice

Cited by in corpus (12)

• Logical quantum processor based on reconfigurable atom arrays
• Sparse Sachdev-Ye-Kitaev model, quantum chaos and gravity duals
• Tridiagonal Hamiltonians modeling the density of states of the Double-Scaled SYK model
• Interacting Thermofield Doubles and Critical Behavior in Random Regular Graphs
• $Q$-Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model
• Parisi's hypercube, Fock-space frustration and near-AdS${}_2$/near-CFT${}_1$ holography
• Parisi's hypercube, Fock-space fluxes, and the microscopics of near-AdS${}_2$/near-CFT${}_1$ duality
• Wavefunction structure in quantum many-fermion systems with $k$-body interactions: conditional $q$-normal form of strength functions
• How to realize compact and non-compact localized states in disorder-free hypercube networks
• Distribution of lowest eigenvalue in $k$-body bosonic random matrix ensembles
• Bosonic near-CFT${}_1$ models from Fock-space fluxes
• Beyond the ensemble paradigm in low dimensional quantum gravity: Schwarzian density, quantum chaos and wormhole contributions