相关论文: Disorder perturbed Flat Bands I: Level density and…
The flattening of single-particle band structures plays an important role in the quest for novel quantum states of matter due to the crucial role of interactions. Recent advances in theory and experiment made it possible to construct and…
Broadly distributed random variables with a power-law distribution $f(m) \sim m^{-(1+\alpha)}$ are known to generate condensation effects, in the sense that, when the exponent $\alpha$ lies in a certain interval, the largest variable in a…
We explore the influence of an arbitrary external potential perturbation V on the spectral properties of a weakly disordered conductor. In the framework of a statistical field theory of a nonlinear sigma-model type we find, depending on the…
In ${\cal PT}-$symmetric quantum mechanics one of the most characteristic mathematical features of the formalism is the explicit Hamiltonian-dependence of the physical Hilbert space of states ${\cal H}={\cal H}(H)$. Some of the most…
We provide a brief overview of approaches for calculating the density of states of quantum systems and random matrix Hamiltonians using the tools of free probability theory. For a given Hamiltonian of a quantum system or a generic random…
Level statistics of systems that undergo many--body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between…
We examine a one-dimensional $\mathcal{PT}$-symmetric binary lattice in the presence of diagonal disorder. We focus on the wave transport phenomena of localized and extended input beams for this disordered system. In the pure…
The effect of strong disorder on chiral-symmetric 3-dimensional lattice models is investigated via analytical and numerical methods. The phase diagrams of the models are computed using the non-commutative winding number, as functions of…
A platform that serves as an ideal playground for realizing ``high'' temperature superconductors are materials where the electrons' kinetic energy is completely quenched, and interactions provide the only energy scale in the problem for…
Highly mismatched alloys (HMAs) have band structures strongly modified due to the introduction of the alloying element. We consider HMAs where the isolated state of the alloying element is near the host conduction band, which causes the…
For two-dimensional Lieb lattice, while intrinsic spin-orbit coupling is responsible for opening the gap that exhibits the quantum spin Hall effect, topological phase transitions are driven by a real next-nearest-neighbor (NNN) hopping. In…
Using the tight-binding model, we investigate the influence of vacancy disorder on electrical transport in graphene Hall bars in the presence of quantizing magnetic fields. Disorder, induced by a random distribution of monovacancies, breaks…
We develop a theory for the compressibility and quantum capacitance of disordered monolayer and bilayer graphene including the full hyperbolic band structure and band gap in the latter case. We include the effects of disorder in our theory,…
We investigate disordered one- and two-dimensional Heisenberg spin lattices across a transition from integrability to quantum chaos from both a statistical many-body and a quantum-information perspective. Special emphasis is devoted to…
Using a numerical implementation of strong disorder renormalization group, we study the low-energy, long-distance properties of layers and bilayers of $S = 1/2$ Heisenberg antiferromagnets with different type of disorder: bond randomness,…
We determine the propagation properties of a quantum particle in a d-dimensional lattice with hopping disorder, delta-correlated in time. The system is delocalized: the averaged transition probability shows a diffusive behavior. Then,…
We study the transport dynamics of matter-waves in the presence of disorder and nonlinearity. An atomic Bose-Einstein condensate that is localized in a quasiperiodic lattice in the absence of atom-atom interaction shows instead a slow…
A generalization of Brillouin-Wigner perturbation theory is applied numerically to the Wigner Band Random Matrix model. The perturbation theory tells that a perturbed energy eigenstate can be divided into a perturbative part and a…
A microscopic statistical model of a quantum solid is developed, where inside a crystalline lattice there can exist regions of disorder, such as dislocation networks or grain boundaries. The cores of these regions of disorder are allowed…
The spectral properties of a disordered system with few interacting three-dimensional spinless fermions are investigated. We show the existence of a critical spacings distribution which is invariant upon increase of the system size, but…