Spectrum statistics in the integrable Lieb-Liniger model
arXiv:2105.02967 · doi:10.1103/PhysRevE.104.034212
Abstract
We address the old and widely debated question of the statistical properties of integrable quantum systems, through the analysis of the paradigmatic Lieb-Liniger model. This quantum many-body model of 1-d interacting bosons allows for the rigorous determination of energy spectra via the Bethe ansatz approach and our interest is understanding whether Poisson statistics is a characteristic feature of this model. Using both analytical and numerical studies we show that the properties of spectra strongly depend on whether the analysis is done for a full energy spectrum or for a single subset with fixed total momentum. We show that the Poisson distribution of spacing between nearest-neighbor energies can occur only for a set of energy levels with fixed total momentum, for neither too large nor too weak interaction strength, and for sufficiently high energy. On the other hand, when studying long-range correlations between energy levels, we found strong deviations from the predictions given by a Poisson process.
12 pages, 7 figures
References in corpus (16)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
- Localization of interacting fermions at high temperature
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Realization of Bose-Einstein condensates in lower dimensions
- Quantum Inverse Scattering Method and Correlation Functions
- An introduction to integrable techniques for one-dimensional quantum systems
- Diffusion and localization in chaotic billiards
- Poisson to GOE transition in the distribution of the ratio of consecutive level spacings
- Nuclei, Primes and the Random Matrix Connection
- Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis
- Distribution of the Ratio of Consecutive Level Spacings for Different Symmetries and Degrees of Chaos
- Momentum distribution of a freely expanding Lieb-Liniger gas
- Wigner--Dyson statistics for a class of integrable models
- Quantum quench dynamics of the attractive one-dimensional Bose gas via the coordinate Bethe ansatz