Related papers: The landscape law for tight binding Hamiltonians
We prove that the the density of states measure (DOSm) for random Schr\"odinger operators on $\mathbb{Z}^d$ is weak-$^*$ H\"older-continuous in the probability measure. The framework we develop is general enough to extend to a wide range of…
We discuss a new strategy for treating the complex action problem of lattice field theories with a $\theta$-term based on density of states (DoS) methods. The key ingredient is to use open boundary conditions where the topological charge is…
These lectures present some basic ideas and techniques in the spectral analysis of lattice Schrodinger operators with disordered potentials. In contrast to the classical Anderson tight binding model, the randomness is also allowed to…
We examine extended bound states in the dilute limit of the extended Hubbard model with next-nearest-neighbour (nnn) hopping and nnn interactions on the two dimensional square lattice. By the exact solution of a two-body problem we show…
The set of continuous norm-preserving stochastic Schrodinger equations associated with the Lindblad master equation is introduced. This set is used to describe the localization properties of the state vector toward eigenstates of the…
We extend our results in \cite{hislop_marx_1} on the quantitative continuity properties, with respect to the single-site probability measure, of the density of states measure and the integrated density of states for random Schr\"odinger…
An exact description of the complete jamming landscape is developed for a system of hard discs of diameter $\sigma$, confined between two lines separated by a distance $1+\sqrt{3/4} < H/\sigma < 2$. By considering all possible local packing…
Using a recently introduced tensor network method, we study the density of states of the lattice Schwinger model, a standard testbench for lattice gauge theory numerical techniques, but also the object of recent experimental quantum…
We study the local behavior of solutions of the stationary Schr\" od\-inger equation with singular potentials, establishing a local decomposition into a homogeneous harmonic polynomial and a lower order term. Combining a corollary to this…
We consider the mapping of tight-binding electronic structure theory to a local spin Hamiltonian, based on the adiabatic approximation for spin degrees of freedom in itinerant-electron systems. Local spin Hamiltonians are introduced in…
States which minimize the Schr\"odinger--Robertson uncertainty relation are constructed as eigenstates of an operator which is a element of the $h(1) \oplus \su(2)$ algebra. The relations with supercoherent and supersqueezed states of the…
We calculate entanglement entropy in a non-relativistic field theory described by the Schr\"odinger operator. We demonstrate that the entropy is characterized by i) the area law and ii) UV divergences that are identical to those in the…
We prove the existence of localized states at the edges of the bands for the two-dimensional Landau Hamiltonian with a random potential, of arbitrary disorder, provided that the magnetic field is sufficiently large. The corresponding…
In the theory of Anderson localization, a landscape function predicts where wave functions localize in a disordered medium, without requiring the solution of an eigenvalue problem. It is known how to construct the localization landscape for…
The localization subregions of stationary waves in continuous disordered media have been recently demonstrated to be governed by a hidden landscape that is the solution of a Dirichlet problem expressed with the wave operator. In this…
We survey recent results on spectral properties of random Schr\"odinger operators. The focus is set on the integrated density of states (IDS). First we present a proof of the existence of a self-averaging IDS which is general enough to be…
We propose a robust and efficient algorithm for computing bound states of infinite tight-binding systems that are made up of a finite scattering region connected to semi-infinite leads. Our method uses wave matching in close analogy to the…
The localization landscape gives direct access to the localization of bottom-of-band eigenstates in non-interacting disordered systems. We generalize this approach to eigenstates at arbitrary energies in systems with or without internal…
The entanglement entropy of a free scalar field in its ground state is dominated by an area law term. It is noteworthy, however, that the study of entanglement in scalar field theory has not advanced far beyond the ground state. In this…
We study ergodic random Schr"odinger operators on a covering manifold, where the randomness enters both via the potential and the metric. We prove measurability of the random operators, almost sure constancy of their spectral properties,…