Quantum Chaos on Edge

Abstract

In recent years, the physics of many-body quantum chaotic systems close to their ground states has come under intensified scrutiny. Such studies are motivated by the emergence of model systems exhibiting chaotic fluctuations throughout the entire spectrum (the Sachdev-Ye-Kitaev (SYK) model being a renowned representative) as well as by the physics of holographic principles, which likewise unfold close to ground states. Interpreting the edge of the spectrum as a quantum critical point, here we combine a wide range of analytical and numerical methods to the identification and comprehensive description of two different universality classes: the near edge physics of ``sparse'' and the near edge of ``dense'' chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension, which is exponentially small or algebraically small in the sparse and dense case, respectively. Notable representatives of the two classes are generic chaotic many-body models (sparse) and single particle systems, invariant random matrix ensembles, or chaotic gravitational systems (dense). While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different. Considering the SYK model as a representative of the sparse class, we apply a combination of field theory and exact diagonalization to a detailed discussion of its edge spectrum. Conversely, Jackiw-Teitelboim gravity is our reference model for the dense class, where an analysis of the gravitational path integral and random matrix theory reveal universal differences to the sparse class, whose implications for the construction of holographic principles we discuss.

arXiv comment22 pages, 11 figures

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Cited by in corpus (8)

• Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
• Quantum feedback induced entanglement relaxation and dynamical phase transition in monitored free fermion chains with Wannier-Stark ladder
• Universal relations between thermoelectrics and noise in mesoscopic transport across a tunnel junction
• Two-local modifications of SYK model with quantum chaos
• Distribution of lowest eigenvalue in $k$-body bosonic random matrix ensembles
• The universality class of the first levels in low-dimensional gravity
• Noise signatures of a charged Sachdev-Ye-Kitaev dot in mesoscopic transport
• q-Gaussian Crossover in Overlap Spectra towards 3D Edwards-Anderson Criticality