Related papers: Ward type identities for the 2d Anderson model at …
We consider the two-level correlation function in two-dimensional disordered systems. In the non-ergodic diffusive regime, at energy $\epsilon>E_{c}$ ($E_{c}$ is the Thouless energy), it is shown to be completely determined by the weak…
We prove exponential spectral localization in a two-particle lattice Anderson model, with a short-range interaction and external random i.i.d. potential, at sufficiently low energies. The proof is based on the multi-particle multi-scale…
We provide an analytic theory of Anderson localization on a lattice with a weak short-range correlated disordered potential. Contrary to the general belief we demonstrate that even next-neighbor statistical correlations in the potential can…
We show that, in contrast to immediate intuition, Anderson localization of noninteracting particles induced by a disordered potential in free space can increase (i.e., the localization length can decrease) when the particle energy…
We revisit the modular weights in type IIB magnetized D-brane models. The simple analysis of wave function shows that the four-dimensional matter fields have the modular weight -1/2, but it may shift as one in type IIA intersecting D-brane…
It is known that in low dimensions WDVV equations can be rewritten as commuting quasilinear bi-Hamiltonian systems. We extend some of these results to arbitrary dimension $N$ and arbitrary scalar product $\eta$. In particular, we show that…
Motivated by experimental progress in cold atomic systems, we use and advance Localisation Landscape Theory (LLT), to examine two-dimensional systems with point-like random scatterers. We begin by showing that exact eigenstates cannot be…
We prove variationally that at weak coupling in one, two, and three dimensions there exist correlated electron-phonon states below the approximate ground states characteristically found by adiabatic polaron theory. Besides differing…
We discovered novel Anderson localization behaviors of pseudospin systems in a 1D disordered potential. For a pseudospin-1 system, due to the absence of backscattering under normal incidence and the presence of a conical band structure, the…
We investigate charge fluctuations in the two-dimensional Hubbard model as a function of doping, interaction strength, next-nearest-neighbor hopping, and temperature within the eight-site dynamical cluster approximation. In the regime of…
We study the effect of electromagnetic interactions on the classical soft theorems on an asymptotically AdS background in 4 spacetime dimensions, in the limit of a small cosmological constant or equivalently a large AdS radius $l$. This…
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
We study deterministic power-law quantum hopping model with an amplitude $J(r) \propto - r^{-\beta}$ and local Gaussian disorder in low dimensions $d=1,2$ under the condition $d < \beta < 3d/2$. We demonstrate unusual combination of…
Ward identities for extended objects are discussed. In the limit of dc transport it is rigorously proved that charge-density and spin-density fluctuations do not couple to electromagnetic field.
In half-filled high Landau levels, two-dimensional electron systems possess collective phases which exhibit a strongly anisotropic resistivity tensor. A weak, but as yet unknown, rotational symmetry-breaking potential native to the host…
A new method of constructing a weak coupling expansion of two dimensional (2D) models with an unbroken continuous symmetry is developed. The method is based on an analogy with the abelian XY model, respects the Mermin-Wagner (MW) theorem…
We derive the anomalous conformal Ward identities for ${\cal N}=4$ SYM Wilson loops on polygon-like contours with edges formed by circular arcs. With a suitable choice of parameterisation they are very similarly to those for local…
Interacting quantum spin models are remarkably useful for describing different types of physical, chemical, and biological systems. Significant understanding of their equilibrium properties has been achieved to date, especially for the case…
We study two interacting electrons in a two-dimensional system under a strong magnetic field and show that their numerically exact solutions organize into a set of {\em sub-Landau levels} characterized by relative angular momentum quantum…
We study localization in two- and three channel quasi-1D systems using multichain tight-binding Anderson models with nearest-neighbour interchain hopping. In the three chain case we discuss both the case of free- and that of periodic…