This site uses cookies. This is a clear signature of quantum chaos. In integrable regimes, on the other hand, the Poisson distribution results in. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. There are some momentum sectors that exhibit space symmetries. (2008). The results for both quantities are not only qualitatively but also quantitatively similar. A system is said to be quantum chaotic if the distribution of normalized energy level spacings follows a Wigner-Dyson function, which exhibits level repulsion Bohigas et al. While many systematic studies of these topics have been undertaken in one-dimensional lattices Rigol (2009a, b); Santos and Rigol (2010b, a); Neuenhahn and Marquardt (2012); Genway et al. systems,”, C. Neuenhahn and F. Marquardt, “Thermalization of interacting fermions and delocalization in Fock in the post Ground state degeneracy: Spin vs Fermionic language; in particular, the discussion below the answer lists some references where the derivation is carried out.. Rev. phases and transitions in transverse Ising models, R. M. Stratt, “Path-integral site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. (2014), this was shown to be the case for observables in various one-dimensional models (including the TFIM with a longitudinal field) when taking the central half of the energy eigenstates. You will only need to do this once. The presentation is organized as follows: In Sec. They are in very good agreement with PGOE(r). Evaluating the quality of Monte Carlo simulations for 3D Ising model, Magnetization in Quantum Transverse Ising Model: Mean Field Theory vs Reality, OOP implementation of Rock Paper Scissors game logic in Java, What modern innovations have been/are being made for the piano. Brown, N. Frazier, and M. Horoi, “The nuclear shell model as a testing In this work, we present an in depth study of quantum chaos and eigenstate thermalization indicators in the 2D-TFIM in the square lattice. Mod. At low temperature, the Peierls argument proves positive magnetization for the nearest neighbor case and then, by the Griffiths inequality, also when longer range interactions are added. 4 when ε=g≈2. High temperature expansion,”, P. Pfeuty and R. J. Elliott, “The Ising In order to check whether eigenstate thermalization occurs in the models studied in Sec. Why is the concept of injective functions difficult for my students? One can then say that, as the system size increases, the eigenstates with energies Eα