ترغب بنشر مسار تعليمي؟ اضغط هنا

Anderson localization on the Bethe lattice: non-ergodicity of extended states

387   0   0.0 ( 0 )
 نشر من قبل Andrea De Luca
 تاريخ النشر 2014
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal dimensions $f(alpha)$ defined in Eq.(3), remains positive for $alpha$ noticeably far from 1 even when the disorder is several times weaker than the one which leads to the Anderson localization, i.e. the ergodicity can be reached only in the absence of disorder. The one-particle multifractality on the Bethe lattice signals on a possible inapplicability of the equipartition law to a generic many-body quantum system as long as it remains isolated.



قيم البحث

اقرأ أيضاً

We study the spectral properties of $D$-dimensional $N=2$ supersymmetric lattice models. We find systematic departures from the eigenstate thermalization hypothesis (ETH) in the form of a degenerate set of ETH-violating supersymmetric (SUSY) doublets , also referred to as many-body scars, that we construct analytically. These states are stable against arbitrary SUSY-preserving perturbations, including inhomogeneous couplings. For the specific case of two-leg ladders, we provide extensive numerical evidence that shows how those states are the only ones violating the ETH, and discuss their robustness to SUSY-violating perturbations. Our work suggests a generic mechanism to stabilize quantum many-body scars in lattice models in arbitrary dimensions.
We present a thorough numerical study of the Richardson model with quenched disorder (a fully-connected XX-model with longitudinal random fields). We study the onset of delocalization in typical states (many-body delocalization) and the delocalized p hase which extends over the whole range of coupling strength in the thermodynamic limit. We find a relation between the inverse participation ratio, the Edwards-Anderson order parameter and the average Hamming distance between spin configurations covered by a typical eigenstate for which we conjecture a remarkably simple form for the thermodynamic limit. We also studied the random process defined by the spread of a typical eigenstate on configuration space, highlighting several similarities with hopping on percolated hypercube, a process used to mimic the slow relaxation of spin glasses.
We discuss symmetry breaking quantum phase transitions on the oft studied Bethe lattice in the context of the ferromagnetic scalar spherical model or, equivalently, the infinite $N_f$ limit of ferromagnetic models with $O(N_f)$ symmetry. We show that the approach to quantum criticality is characterized by the vanishing of a gap to just the global modes so that {it all} local correlation functions continue to exhibit massive behavior. This behavior persists into the broken symmetry phase even as the order parameter develops an expectation value and thus there are no massless Goldstone bosons in the spectrum. We relate this feature to a spectral property of the graph Laplacian shared by the set of `expander graphs, and argue that our results apply to symmetry breaking transitions on such graphs quite generally.
We introduce a new two-dimensional model with diagonal four spin exchange and an exactly knownground-state. Using variational ansaetze and exact diagonalisation we calculate upper and lower bounds for the critical coupling of the model. Both for this model and for the Shastry-Sutherland model we study periodic systems up to system size 6x6.
We observe a localized phase of ultracold bosonic quantum gases in a 3-dimensional optical lattice induced by a small contribution of fermionic atoms acting as impurities in a Fermi-Bose quantum gas mixture. In particular we study the dependence of t his transition on the fermionic 40K impurity concentration by a comparison to the corresponding superfluid to Mott insulator transition in a pure bosonic 87Rb gas and find a significant shift in the transition parameter. The observed shift is larger than expected based on a mean-field argument, which is a strong indication that disorder-related effects play a significant role.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا