Quantum chaos, localized states and clustering in excited spectra of Jahn–Teller models

We numerically studied complex excited spectra and their statistical characteristics of spin- two boson systems represented by the E ⊗ e and E ⊗ (b1 + b2) Jahn–Teller models. For the E ⊗ e system at particular rotation quantum numbers we found a coexistence of up to three regions of the spectra, (i) the dimerized region of long-range ordered (extended) pairs of oscillating levels, (ii) the short-range ordered (localized) “kink lattice” of avoiding levels, and (iii) the intermediate region of kink nucleation with variable range of ordering. This structure appears above a certain critical line as a function of interaction strength. The level clustering (dimerization and trimerization) and level avoiding generic patterns reflect themselves in several intermittent regions between up-to three branches of spectral entropies corresponding to up-to three nonequivalent effective potential wells. We found that apart from two limiting cases of E ⊗ (b1 + b2) system (E ⊗ e and Holstein model) the distribution of nearest neighbor spacings of this model is rather stable as to the change of parameters and different from Wigner one. This limiting distribution assumably shows scaling ∼ S at small S and resembles the semi-Poisson law P(S) = 4S exp(−2S) at S ⩾ 1. The latter is believed to be characteristic, e.g., at the transition between metal and insulator phases of the Anderson model of disorder.