Distribution of the ratio of consecutive level spacings in random matrix ensembles.

By Y. Y. Atas, E. Bogomolny, O. Giraud, G. Roux. Physical Review Letters, 2012

799 citations recorded by the source corpus.

We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body problems, as, contrary to the standard level spacing distributions, it does not depend on the local density of states. Our Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit. Quantitative improvements are found through a polynomial expansion. Examples from a quantum many-body lattice model and from zeros of the Riemann zeta function are presented.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/545d0bedb5e3f828bfb6a562d55569c570c50650

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. V. Khemani
2. Tomaz Prosen
3. Pedro Ribeiro
4. Lucas S'a
5. Anushya Chandran
6. J. Bonvca
7. R. Shir
8. Jan vSuntajs

In Condensed Matter Physics

1. V. Khemani
2. J. Bonvca
3. R. Shir
4. Jan vSuntajs
5. Heng Fan
6. Anushya Chandran
7. Junyu Liu
8. Yuan Xin

Citations in the corpus

• Quantum Entanglement in Neural Network States (2017, neutral): “386 [107].”
• Signatures of integrability in the dynamics of Rydberg-blockaded chains (2018, methodology): “53 otherwise[36].”
• Avalanches and many-body resonances in many-body localized systems (2021, neutral): “5307 [77].”
• Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos (2019, methodology): “[85, 86], analytic expressions for the ratio distributions were obtained, including Wigner-like surmises for 3 × 3 matrices.”
• Ergodicity breaking transition in finite disordered spin chains (2020, background): “5307 [112], while at large W in finite systems, S → 0 [37] and r → rPoisson = 2 ln(2)− 1 ≈ 0.”
• Krylov complexity from integrability to chaos (2022, methodology): “We will demonstrate the transition from integrability to chaos by studying the distribution of the ratios of consecutive level spacings [40, 41], and show that increasing the strength of the integrability breaking term from zero will result in a transition in the spectral behaviour from integrable t”
• Quantum coherence and geometric quantum discord (2017, background): “In thermal phase, the energy levels of the system tend to repel one another and their statistics are Wigner-Dyson distribution, while for many-body localized state, the energy levels show a Poisson statistics (Atas et al., 2013; Bohigas et al., 1984; Oganesyan and Huse, 2007).”
• Supersymmetric SYK model and random matrix theory (2017, methodology): “For matrices from the standard Dyson ensemble, the distribution of level spacing ratio satisfies the Wigner-Dyson statistics [80] (which is called the Wigner surmise)”