Non-Universal Behavior of the k-Body Embedded Gaussian Unitary Ensemble of Random Matrices

Abstract

Using a novel approach, we investigate the shape of the average spectrum and the spectral fluctuations of the $k$-body embedded unitary ensemble in the limit of large matrix dimension. We identify the transition point between semicircle and Gaussian shape. The transition also affects the spectral fluctuations which deviate from Wigner-Dyson form and become Poissonian in the limit $k<<m<<l$. Here $m$ is the number of Fermions and $l$ the number of degenerate single-particle states.

4 pages, no figures, revised version including a new proof of one of our main claims

Cited by in corpus (36)

• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems
• Review of the k-Body Embedded Ensembles of Gaussian Random Matrices
• Sparse Sachdev-Ye-Kitaev model, quantum chaos and gravity duals
• Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$
• Semiclassical roots of universality in many-body quantum chaos
• Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons
• Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions
• Ground-State Magnetization for Interacting Fermions in a Disordered Potential : Kinetic Energy, Exchange Interaction and Off-Diagonal Fluctuations
• Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model
• Non-Ergodic Behaviour of the k-Body Embedded Gaussian Random Ensembles for Bosons
• Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model
• Strength functions, entropies and duality in weakly to strongly interacting fermionic systems
• SU(N) Wigner-Racah algebra for the matrix of second moments of embedded Gaussian unitary ensemble of random matrices
• Origin of chaos in the spherical nuclear shell model: role of symmetries
• Symmetry Properties of the k-Body Embedded Unitary Ensemble of Random Matrices
• Large $N$ expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs
• Spectral statistics of the k-body random-interaction model
• Supersymmetry method for interacting chaotic and disordered systems: the SYK model
• Particle Diagrams and Statistics of Many-Body Random Potentials
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Program in C for studying characteristic properties of two-body interactions in the framework of spectral distribution theory
• Random Matrix Ensembles For Many-Body Quantum Systems
• Particle diagrams and embedded many-body random matrix theory
• Characterizing quantum chaoticity of kicked spin chains
• Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model
• Bivariate moments of the two-point correlation function for embedded Gaussian unitary ensemble with $k$-body interactions
• Localization Properties of Two Interacting Electrons in a Disordered Quasi One-Dimensional Potential
• Two Interacting Electrons in a Disorder Potential: Localization Properties
• The Topological Non-connectivity Threshold in quantum long-range interacting spin systems
• Random matrix ensembles with random interactions: Results for EGUE(2)-SU(4)
• Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model
• Euclidean-to-Lorentzian wormhole transition and gravitational symmetry breaking in the Sachdev-Ye-Kitaev model
• Volume-law entanglement entropy of typical pure quantum states
• Normal mode analysis of disordered random-matrix ensembles
• Fold bifurcation entangled surfaces for one-dimensional Kitaev lattice model