While there are well established methods to study delocalization transitions of single particles in random systems, it remains a challenging problem how to characterize many body delocalization transitions. Here, we use a generalized real-space renor
malization group technique to study the anisotropic Heisenberg model with long-range interactions, decaying with a power $alpha$, which are generated by placing spins at random positions along the chain. This method permits a large-scale finite-size scaling analysis. We examine the full distribution function of the excitation energy gap from the ground state and observe a crossover with decreasing $alpha$. At $alpha_c$ the full distribution coincides with a critical function. Thereby, we find strong evidence for the existence of a many body localization transition in disordered antiferromagnetic spin chains with long range interactions.
We present a numerical study of a quantum phase transition from a spin-polarized to a topologically ordered phase in a system of spin-1/2 particles on a torus. We demonstrate that this non-symmetry-breaking topological quantum phase transition (TOQPT
) is of second order. The transition is analyzed via the ground state energy and fidelity, block entanglement, Wilson loops, and the recently proposed topological entropy. Only the topological entropy distinguishes the TOQPT from a standard QPT, and remarkably, does so already for small system sizes. Thus the topological entropy serves as a proper order parameter. We demonstrate that our conclusions are robust under the addition of random perturbations, not only in the topological phase, but also in the spin polarized phase and even at the critical point.
We have synthesized, crystallized and studied the structural and electric transport properties of organic molecular crystals based on a rubrene derivative with {em t}-butyl sidegroups at the 5,11 positions. Two crystalline modifications are observed:
one (A) distinct from that of rubrene with larger spacings between the naphtacene backbones, the other (B) with a in-plane structure presumably very similar compared to rubrene. The electric transport properties reflect the different structures: in the latter phase (B) the in-plane hole mobility of 12 cm$^2$/Vs measured on single crystal FETs is just as high as in rubrene crystals, while in the A phase no field-effect could be measured. The high crystal quality, studied in detail for B, reflects itself in the density of gap states: The deep-level trap density as low as $10^{15}$ cm$^{-3}$ eV$^{-1}$ has been measured, and an exponential band tail with a characteristic energy of 22 meV is observed. The bulk mobility perpendicular to the molecular planes is estimated to be of order of $10^{-3}$ -- $10^{-1}$ cm$^2$/Vs.
The uniaxial negative thermal expansion in pentacene crystals along $a$ is a particularity in the series of the oligoacenes, and exeptionally large for a crystalline solid. Full x-ray structure analysis from 120 K to 413 K reveals that the dominant t
hermal motion is a libration of the rigid molecules about their long axes, modifying the intermolecular angle which describes the herringbone packing within the layers. This herringbone angle increases with temperature (by 0.3 -- 0.6$^{circ}$ per 100 K), and causes an anisotropic rearrangement of the molecules within the layers, i.e. an expansion in the $b$ direction, and a distinct contraction along $a$. Additionally, a larger herringbone angle improves the cofacial overlap between adjacent, parallel molecules, and thus enhances the attractive van der Waals forces.
The density of trap states in the bandgap of semiconducting organic single crystals has been measured quantitatively and with high energy resolution by means of the experimental method of temperature-dependent space-charge-limited-current spectroscop
y (TD-SCLC). This spectroscopy has been applied to study bulk rubrene single crystals, which are shown by this technique to be of high chemical and structural quality. A density of deep trap states as low as ~ 10^{15} cm^{-3} is measured in the purest crystals, and the exponentially varying shallow trap density near the band edge could be identified (1 decade in the density of states per ~25 meV). Furthermore, we have induced and spectroscopically identified an oxygen related sharp hole bulk trap state at 0.27 eV above the valence band.
