You can find more about that e.g. It was examined by two of us (KRF and MS) Fratus and Srednicki (2015) to understand whether eigenstate thermalization Deutsch (1991); Srednicki (1994); Rigol et al. quantum thermalization,” Phys. function structure in two-body random matrix ensembles,” Phys. Note that, away from the integrable limits g=0 and g=∞, the results are consistent with ⟨r⟩GOE. Section IV is devoted to the analysis of eigenstate thermalization indicators and their scaling. On the other hand, as per Berry-Tabor’s conjecture Berry and Tabor (1977), one expects a Poisson distribution when the system is integrable. Journal of Physics C: Solid State Physics, We compute. R. Ma, M. E. Tai, P. M. Preiss,  and M. Greiner, “Quantum simulation of antiferromagnetic spin chains in an optical It features a lattice with nearest neighbour interactions determined by the alignment or anti-alignment of spin projections along the $${\displaystyle z}$$ axis, as well as an external magnetic field perpendicular to the $${\displaystyle z}$$ axis (without loss of generality, along the $${\displaystyle x}$$ axis) which creates an energetic bias for one x-axis spin direction over the other. C: Solid State Phys. Brown, N. Frazier,  and M. Horoi, “The nuclear shell model as a testing We also note that the cluster 20B (see Fig. (2011); Foini et al. Given Tc, one can calculate the mean energy of the system, Ec, at that temperature: where we have set the Boltzmann constant to one. J is the strength of the nearest neighbor (⟨i,j⟩ in the summation) Ising interaction. The transverse field Ising model (TFIM) is one of the simplest models that exhibits both ground-state and finite-temperature (in dimensions higher than one) phase transitions between paramagnetic and ordered phases. The better we are at sharing our knowledge with each other, the faster we move forward. I. The decrease of the average value is consistent with an exponential for the systems with N≥12, independent of the value of xthr. The leading-order approximations for the correlation functions, susceptibilities and spectral functions are discussed in detail. 3 and 4, we show the structural entropy for the ferromagnetic and antiferromagnetic models, respectively, for five different systems sizes and eight values of the transverse field. 3 and 4, one can see that as one departs from the integrable limits g=0 and g=∞, and as one increases the system size, the eigenstate expectation values away from the edges of the spectrum become a smoother function of the eigenstate energies. Published under licence by IOP Publishing Ltd Meanwhile, at high temperature, the cluster expansion gives analyticity of the thermodynamic functions. We report results for the largest, the fifth largest, and the tenth largest values of those quantities in the windows selected, as well as the average value (which is dominated by the aforementioned “infinite-temperature” states). and the inverse participation ratio (IPR). quenches in the transverse field Ising chain: II. This highlights the importance of resolving all symmetries for one to be able to identify the presence of quantum chaos in the distribution of level spacings. The insets in Fig. effects of fluctuations,”, Journal of Physics C: Solid State Physics. In the momentum sectors with k=(0,0) and k=(π,π), Fig. in the transverse-field Ising chain,”, L. Foini, L. F. Cugliandolo,  and A. Gambassi, “Fluctuation-dissipation relations and critical quenches in the transverse In this Course, we will restrict to the study of classical statistical systems at equilibrium, in two dimensions. We study the onset of eigenstate thermalization in the two-dimensional transverse field Ising model (2D-TFIM) in the square lattice. g and ε are the strength of the transverse and longitudinal fields, respectively. Elliott et al. two-body random ensemble revisited,” Phys. We note that, the highly symmetric clusters with 16 and 18 sites [P(r) is not shown for those clusters] exhibit space symmetries (not necessarily inversion) in all momentum sectors. We consider two non-equivalent Hamiltonians: the ferromagnetic 2D-TFIM and the antiferromagnetic 2D-TFIM in the presence of a uniform longitudinal field. rev 2020.11.24.38066, The best answers are voted up and rise to the top, Physics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Analytical solution to 1D transverse Ising model, Ground state degeneracy: Spin vs Fermionic language, “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM….