The level statistics of random spin ½ XY chain model

Different level spacing distributions such as Poisson distribution and Gaussian orthogonal ensemble(GOE) have been used to characterize many-body localization in random quantum systems. For simple quantum many-body systems, the energy level spacing can be obtained by exact diagonalization studies[1, 2]. However, because of heavy computation cost, not all eigenstates can be taken into account in exact diagonalization studies of many-body quantum systems with even moderate sizes. In this talk, we investigate a spin 1/2 random xy chain model where all eigenstates can be obtained up to rather large system size. we find that for high enough disorder, the energy level distribution approaches a Poisson distribution, in agreement with previous results. However, there exists a gapped region where neither Poisson nor GOE are found in weak disorder.
[1] Arijeet Pal and David A. Huse, Phys. Rev. B 82, 174411 (2010).
[2] Rahul Nandkishore and David A. Huse, Annual Review of Condensed Matter Physics 6, 15–38 (2015)